Quiz:Symmetric group:S5

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See symmetric group:S5. We take the symmetric group on the set \! \{ 1,2,3,4,5 \} of size five.

Elements

See element structure of symmetric group:S5 for full details.

Element orders and conjugacy class structure

Review the conjugacy class structure: [SHOW MORE]

1 What is the maximum among the orders of elements of the symmetric group of degree five?

5
6
8
10
12

2 What is the exponent of the symmetric group of degree five, i.e., the least common multiple of the orders of all elements of this group?

10
20
30
60
120

Subgroups

See subgroup structure of symmetric group:S5 for background information and more details.

Basic stuff

Summary table on the structure of subgroups: [SHOW MORE]

1 For which of the following divisors of 120 does there not exist a subgroup of the symmetric group of degree five with that as order?

12
20
24
30
60

2 What is the smallest possible order of a group that is not isomorphic to any subgroup of the symmetric group of degree five?

5
6
7
8
9

3 What is the smallest possible order of a group that is isomorphic to subgroups in two distinct conjugacy classes of subgroups in the symmetric group of degree five?

2
3
4
5
6