| order | 4608 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | D3×#11714174 |
| Fitting | C3×#3027 ⋊ C2×D3 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D3×#1020⋊C2 |
| commutator, cosocle, hypocenter | C3×#997 | C24 |
| Frattini | C23 | C22×D3×S4 |
| Fitting | C3×#3027 | C2×D3 |
| socle | C2×C3 | C22×#1020⋊C2 |
| hypercenter | C4 | D3×#1020⋊C2 |
| LCS | G ▷ C3×#997 | |
| UCS | C1 ◁ C2 ◁ C4 | |
7541 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
93 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#72217027 |
| maximal normal subgroup of | D3×#72217027 |
Past the SmallGroups library coverage — no SmallGroups id.