Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#47804⋊C3 |
| Fitting, Sylow | C2×#47804 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #3549⋊C3 |
| commutator, cosocle, hypocenter | #2844 | C22×C3 |
| Frattini | C23 | C22×C22⋊A4 |
| Fitting | C2×#47804 | C3 |
| socle | C24 | C2×C22⋊A4 |
| LCS | G ▷ #2844 | |
| UCS | C1 ◁ C22 | |
2049 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 2049 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
56 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.