Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#72236846 |
| Fitting | C2×#21483 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #1020⋊C2 |
| commutator, hypocenter | #997 | C23×C4 |
| Frattini | C22×C4 | C23×S4 |
| Fitting | C2×#21483 | D3 |
| socle | C22 | C4×#1020⋊C2 |
| prime radical | C2×#11714162 | C2 |
| cosocle | #5950 | C24 |
| LCS | G ▷ #997 | |
| UCS | C1 ◁ C2×C8 | |
6393 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #72342856, C2×#72240995, C2×#72240991, … |
| maximal normal subgroup of | #72342856, C2×#72240995, C2×#72240991, … |
Past the SmallGroups library coverage — no SmallGroups id.