Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C2×D11×C32 |
| Fitting | C2×C11×C32 ⋊ C2 |
| derived, Sylow | C11 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D11 |
| commutator, hypocenter | C11 | C22×C32 |
| Frattini | C16 | C22×D11 |
| Fitting | C2×C11×C32 | C2 |
| socle | C22×C11 | C2×C16 |
| prime radical | C22×D11 | C16 |
| cosocle | C11×C16 | C23 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C32 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
448 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C2×D11)⋊C64, C4×D11×C32, D11×#1397, … |
| maximal normal subgroup of | (C2×D11)⋊C64, C4×D11×C32, D11×#1397, … |
| maximal quotient of | C4×D11×C32, C2×C32×Dic11, D11×C22⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6798);