Finite Group DatabasebetaFinite Group Databasebeta| order | 7920 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C22×C3 |
| direct product | A42×C11⋊C5 |
| Fitting, socle, derived, Hall | C24×C11 ⋊ C32×C5 |
| Hall | C11×A42 ⋊ C5 |
| Hall | C24×C11⋊C5 ⋊ C32 |
| Sylow | C24 ⋊ C32×C11⋊C5 |
| Sylow | C11 ⋊ C5×A42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C24×C11 | C32×C5 |
| LCS | G ▷ C24×C11 | |
| UCS | C1 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 132 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | A42×AGL(1,𝔽11), C11⋊C5×A4⋊S4, #72268737 |
| maximal normal subgroup of | A42×AGL(1,𝔽11), C11⋊C5×A4⋊S4, #72268737 |
Past the SmallGroups library coverage — no SmallGroups id.