# 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