Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C27 |
| direct product | C22×#11710348 |
| Fitting, Sylow | C22×#60400 ⋊ C3 |
| derived | 2−1+6 ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C23 | #85645 |
| commutator, cosocle, hypocenter | 2−1+6 | C23×C3 |
| Frattini | C23 | C23×C22⋊A4 |
| Fitting | C22×#60400 | C3 |
| LCS | G ▷ 2−1+6 | |
| UCS | C1 ◁ C23 | |
95745 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 95745 conjugacy classes of subgroups — too many to draw. Only its 164 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 128 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #72266494 |
Past the SmallGroups library coverage — no SmallGroups id.