Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D11×D32 |
| Fitting | C11×D32 ⋊ C2 |
| Sylow | C11 ⋊ C2×D32 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D11×D16 |
| commutator, cosocle | C11×C16 | C23 |
| Frattini | C16 | C22×D11 |
| Fitting | C11×D32 | C2 |
| socle | C2×C11 | C2×D16 |
| hypercenter | D32 | D11 |
| hypocenter | C11 | C2×D32 |
| LCS | G ▷ C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ D32 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
133 conjugacy classes — view the full character table.
| maximal subgroup of | D11×D64, D11×SD128, #14674829, … |
| maximal normal subgroup of | D11×D64, D11×SD128, #14674829, … |
| maximal quotient of | D11×#1415, D11×#1423, #14674344, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6806);