hinte

[tropic hollow]

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[shut stag]

What do you think?

Look at the properties of groups of order 45.

The order of a group G is 45, which can be factorized as 45 = 3^2 × 5

Recall the Sylow thereoms.

[drifting rock]

Yes

Actually I don't understand sylow

[shut stag]

Looks at the first statement.

By Sylow thereoms, the number of Sylow 5 sub groups n5 must divide 9 (since 45/5 = 9) and must be congruent to 1 modulo 5.

The only integer that satisfies these conditions is n5 = 1.

Hence, it's unique and therefore normal (the sylow 5-subgroup)