Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| direct product | D11×C64 |
| Fitting | C11×C64 ⋊ C2 |
| derived, Sylow | C11 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C64 | D11 |
| commutator, hypocenter | C11 | C2×C64 |
| Frattini | C32 | C2×D11 |
| Fitting | C11×C64 | C2 |
| socle | C2×C11 | C2×C32 |
| prime radical | C2×D11 | C32 |
| cosocle | C11×C32 | C22 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C64 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
448 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×C128, #14641683, C2×D11×C64, … |
| maximal normal subgroup of | D11×C128, #14641683, C2×D11×C64, … |
| maximal quotient of | Dic11×C64, (C2×D11)⋊C64, Dic11⋊C64, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2718);