Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C8×Dic179 |
| derived, Sylow | C179 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D179 |
| commutator, hypocenter | C179 | C2×C4×C8 |
| Frattini | C2×C4 | C22×D179 |
| Fitting | C22×C8×C179 | C2 |
| socle, prime radical | C23×C179 | C2×C4 |
| cosocle | C2×C4×C179 | C23 |
| LCS | G ▷ C179 | |
| UCS | C1 ◁ C22×C8 | |
162 conjugacy classes of subgroups.
2912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37507077, #37507081, C4×C8×Dic179, … |
| maximal normal subgroup of | #37507077, #37507081, C4×C8×Dic179, … |
| maximal quotient of | C2×C8×C179⋊C8, C2×#26038161, C8×#15668243, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 494);