Finite Group DatabasebetaFinite Group Databasebeta| order | 4608 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C29 |
| direct product | C22×D3×#5934 |
| Fitting | C22×C3×H(5,𝔽2) ⋊ C2×D3 |
| derived | C3×#997 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D3×#1020 |
| commutator, cosocle, hypocenter | C3×#997 | C24 |
| Frattini | C2 | C22×D3×#1020 |
| Fitting | C22×C3×H(5,𝔽2) | C2×D3 |
| socle | C23×C3 | C2×#1020 |
| LCS | G ▷ C3×#997 | |
| UCS | C1 ◁ C23 | |
47889 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 47889 conjugacy classes of subgroups — too many to draw. Only its 250 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#72209641 |
Past the SmallGroups library coverage — no SmallGroups id.