Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#10623081 |
| Fitting | C2×C4×D4×C11 ⋊ C2 |
| Sylow | C11 ⋊ C2×#546 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D11 |
| commutator, cosocle | C22×C11 | C25 |
| Frattini | C22 | C24×D11 |
| Fitting | C2×C4×D4×C11 | C2 |
| socle | C23×C11 | C24 |
| hypercenter | C2×C4×D4 | D11 |
| hypocenter | C11 | C2×#546 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ C2×C4×D4 | |
1900 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | #14645354, #14645357, #14645394, … |
| maximal normal subgroup of | #14645354, #14645357, #14645394, … |
| maximal quotient of | C2×C22⋊C4×D44, C2×#13071447, C2×#13071459, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 17961);