Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C64 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C179⋊C64 |
| derived, Sylow | C179 ⋊ C64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C32 | D179 |
| commutator, hypocenter | C179 | C64 |
| Fitting, cosocle | C32×C179 | C2 |
| socle, prime radical | C2×C179 | C32 |
| LCS | G ▷ C179 | |
| UCS | C1 ◁ C32 | |
14 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,g^a=g^1782912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C64×D179, C2×C179⋊C64, #37507210, … |
| maximal normal subgroup of | C64×D179, C2×C179⋊C64, #37507210, … |
| maximal quotient of | #37506819, C2×C179⋊C64 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 268);