Finite Group DatabasebetaFinite Group Databasebeta| order | 4608 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C29 |
| direct product | C2×D3×#87588 |
| Fitting, socle | C27×C3 ⋊ C2×D3 |
| derived | C3×C22⋊(C22⋊A4) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×#87588 |
| commutator, cosocle, hypocenter | C3×C22⋊(C22⋊A4) | C23 |
| Frattini | C1 | G |
| Fitting, socle | C27×C3 | C2×D3 |
| LCS | G ▷ C3×C22⋊(C22⋊A4) | |
| UCS | C1 ◁ C2 | |
169874 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 169874 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#87588⋊C2 |
| maximal normal subgroup of | C2×D3×#87588⋊C2 |
| maximal quotient of | C2×D3×#11715850 |
Past the SmallGroups library coverage — no SmallGroups id.