Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C2×#10623121 |
| Fitting | C2×C11×#120 ⋊ C2 |
| Sylow | C11 ⋊ C2×D42 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D11 |
| commutator, cosocle | C22×C11 | C25 |
| Frattini | C22 | C24×D11 |
| Fitting | C2×C11×#120 | C2 |
| socle | C23×C11 | C24 |
| hypercenter | C2×#120 | D11 |
| hypocenter | C11 | C2×D42 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
2536 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
190 conjugacy classes — view the full character table.
| maximal subgroup of | #14669572, #14669573, #14769093, … |
| maximal normal subgroup of | #14669572, #14669573, #14769093, … |
| maximal quotient of | C2×#13071432, C2×#13071434, C2×#13071514, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 17946);