Finite Group DatabasebetaFinite Group Databasebeta| order | 9216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C28 |
| direct product | C2×C3×#72209653 |
| Fitting | C2×C3×#35346 ⋊ D3 |
| derived | C22⋊#997 ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #87588⋊C2 |
| commutator, cosocle, hypocenter | C22⋊#997 | C23×C3 |
| Frattini | C23 | C22×C3×#1020 |
| Fitting | C2×C3×#35346 | D3 |
| socle | C24×C3 | C2×#1020 |
| LCS | G ▷ C22⋊#997 | |
| UCS | C1 ◁ C22×C3 | |
41931 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 41931 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
240 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.