Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×C179⋊C32 |
| unambiguous semidirect product | (C2×C179)⋊C32 |
| derived, Sylow | C179 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | D179 |
| commutator, hypocenter | C179 | C2×C32 |
| Frattini | C16 | C2×D179 |
| Fitting | C2×C16×C179 | C2 |
| socle, prime radical | C22×C179 | C16 |
| cosocle | C16×C179 | C22 |
| LCS | G ▷ C179 | |
| UCS | C1 ◁ C2×C16 | |
34 conjugacy classes of subgroups.
2912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×Dic179, C4×C179⋊C32, #37507133, … |
| maximal normal subgroup of | C32×Dic179, C4×C179⋊C32, #37507133, … |
| maximal quotient of | C4×C179⋊C32, #37507138, #37507196, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 381);