Finite Group DatabasebetaFinite Group Databasebeta| order | 3024 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×#13094716 |
| Hall | C32×ΓL(1,𝔽8) ⋊ C2×D4 |
| Sylow | C7 ⋊ C2×C3×C4⋊(C3⋊D3) |
776 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 776 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 504 |
150 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.