Finite Group DatabasebetaFinite Group Databasebeta| order | 4608 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C27×C3 |
| direct product | C2×#72231670 |
| Fitting | C23×C3×#120 ⋊ D3 |
| derived | C3×C22⋊(C22⋊A4) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72231670 |
| commutator, cosocle, hypocenter | C3×C22⋊(C22⋊A4) | C23 |
| Frattini | C22 | C22×C3⋊#1020 |
| Fitting | C23×C3×#120 | D3 |
| socle | C25×C3 | C2×S4 |
| LCS | G ▷ C3×C22⋊(C22⋊A4) | |
| UCS | C1 ◁ C2 | |
16502 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 16502 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
108 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×#72231672 |
Past the SmallGroups library coverage — no SmallGroups id.