Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C24×Dic179 |
| derived, Sylow | C179 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D179 |
| commutator, hypocenter | C179 | C24×C4 |
| Frattini | C2 | C24×D179 |
| Fitting, socle, prime radical | C25×C179 | C2 |
| cosocle | C2×C179 | C25 |
| LCS | G ▷ C179 | |
| UCS | C1 ◁ C25 | |
1362 conjugacy classes of subgroups.
2912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37507222, C22×C179⋊#95, C2×C22⋊C4×Dic179 |
| maximal normal subgroup of | #37507222, C22×C179⋊#95, C2×C22⋊C4×Dic179 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 1368);