Finite Group DatabasebetaFinite Group Databasebeta| order | 8096 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C24 |
| direct product | #120×C23⋊C11 |
| Fitting, Hall | C23×#120 ⋊ C11 |
| Sylow | C23 ⋊ C11×#120 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×C23⋊C11 |
| commutator, socle, cosocle | C22×C23 | C23×C11 |
| Fitting | C23×#120 | C11 |
| hypercenter | #120 | C23⋊C11 |
| hypocenter | C23 | C11×#120 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ #120 | |
260 conjugacy classes of subgroups.
| transitive degree | μt(G) = 184 |
182 conjugacy classes — view the full character table.
| maximal subgroup of | #120×AGL(1,𝔽23), B(4,𝔽2)×C23⋊C11, #72247938 |
| maximal normal subgroup of | #120×AGL(1,𝔽23), B(4,𝔽2)×C23⋊C11, #72247938 |
| maximal quotient of | #453×C23⋊C11, B(4,𝔽2)×C23⋊C11 |
Past the SmallGroups library coverage — no SmallGroups id.