Finite Group DatabasebetaFinite Group Databasebeta| order | 4608 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
| direct product | C2×D3×#73026 |
| Fitting | C2×C3×B(4,𝔽2) ⋊ C2×D3 |
| derived | C3×#997 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×#1020⋊C2 |
| commutator, cosocle, hypocenter | C3×#997 | C24 |
| Frattini | C23 | C22×D3×S4 |
| Fitting | C2×C3×B(4,𝔽2) | C2×D3 |
| socle | C22×C3 | C2×#1020⋊C2 |
| LCS | G ▷ C3×#997 | |
| UCS | C1 ◁ C22 | |
14227 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 14227 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#72217027, C2×D3×#11757163⋊C2 |
| maximal normal subgroup of | D3×#72217027 |
Past the SmallGroups library coverage — no SmallGroups id.