Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C8×C179⋊C8 |
| unambiguous semidirect product | C179⋊C82 |
| derived, Sylow | C179 ⋊ C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | D179 |
| commutator, hypocenter | C179 | C82 |
| Frattini | C42 | C2×D179 |
| Fitting | C4×C8×C179 | C2 |
| socle, prime radical | C22×C179 | C42 |
| cosocle | C42×C179 | C22 |
| LCS | G ▷ C179 | |
| UCS | C1 ◁ C4×C8 | |
74 conjugacy classes of subgroups.
2912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×C179⋊C8, #37506916, #37506919, … |
| maximal normal subgroup of | C16×C179⋊C8, #37506916, #37506919, … |
| maximal quotient of | #37506827, C16×C179⋊C8, C8×C179⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 269);