Finite Group DatabasebetaFinite Group Databasebeta| order | 4608 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C27×C3 |
| direct product | C2×C3×#11710730 |
| Fitting | C2×C3×#62817 ⋊ C3 |
| derived | #62817 ⋊ C2×C32 |
| Sylow | C2×#62817 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C23×C3 | C22⋊(C22⋊A4) |
| commutator, cosocle, hypocenter | #62817 | C2×C32 |
| Frattini | C22 | C2×C3×C22⋊(C22⋊A4) |
| Fitting | C2×C3×#62817 | C3 |
| LCS | G ▷ #62817 | |
| UCS | C1 ◁ C23×C3 | |
32492 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 32492 conjugacy classes of subgroups — too many to draw. Only its 230 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×#72209641, C2×D3×#11710730, C2×#72230852, … |
| maximal normal subgroup of | C2×C3×#72209641, C2×D3×#11710730, C2×#72230852, … |
Past the SmallGroups library coverage — no SmallGroups id.