Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C213 |
| direct product | C2×#10943958 |
| Fitting | C23×C3×H(5,𝔽2) ⋊ C2 |
| Sylow | C3 ⋊ C2×#32898 |
39956 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
234 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#32898, #72269943, #72270028, … |
| maximal normal subgroup of | C2×D3×#32898, #72269943, #72270028, … |
| maximal quotient of | C2×#72230825, C2×#72219821 |
Past the SmallGroups library coverage — no SmallGroups id.