Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C27 |
| direct product | C2×#72237717 |
| Fitting, Sylow | C2×#8934366 ⋊ C3 |
| derived | #2679 ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #63011⋊C3 |
| commutator, cosocle, hypocenter | #2679 | C23×C3 |
| Frattini | C23 | C23×C22⋊A4 |
| Fitting | C2×#8934366 | C3 |
| socle | C24 | C22×C22⋊A4 |
| LCS | G ▷ #2679 | |
| UCS | C1 ◁ C22 | |
29152 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 29152 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72237738, C2×#72240900, C2×#72240899 |
| maximal normal subgroup of | C2×#72237738, C2×#72240900, C2×#72240899 |
Past the SmallGroups library coverage — no SmallGroups id.