Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C211 |
| direct product | C22×#60399⋊C3 |
| Fitting, Sylow | C22×#60399 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×#120⋊C3 |
| commutator, cosocle, hypocenter | H(5,𝔽2) | C25×C3 |
| Frattini | C23 | C25×A4 |
| Fitting | C22×#60399 | C3 |
| hypercenter | C22×D4 | #120⋊C3 |
| LCS | G ▷ H(5,𝔽2) | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
103026 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#72217027, C2×#72240977, C2×#72240979 |
| maximal normal subgroup of | C22×#72217027, C2×#72240977, C2×#72240979 |
| maximal quotient of | C2×#72246181 |
Past the SmallGroups library coverage — no SmallGroups id.