Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C212 |
| direct product | C22×D4×#120⋊C3 |
| Fitting, Sylow | C22×D4×#120 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×#120⋊C3 |
| commutator, cosocle | C25 | C25×C3 |
| Frattini | C23 | C25×A4 |
| Fitting | C22×D4×#120 | C3 |
| socle | C25 | C23×A4 |
| hypercenter | C22×D4 | #120⋊C3 |
| hypocenter | C24 | C23×C3×D4 |
| LCS | G ▷ C25 ▷ C24 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
186224 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D4×#1020⋊C2 |
| maximal normal subgroup of | C22×D4×#1020⋊C2 |
| maximal quotient of | C2×#72240977 |
Past the SmallGroups library coverage — no SmallGroups id.