Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×(ΓL(1,𝔽8)⋊D7)⋊C4 |
| derived, Sylow | C72 ⋊ C22×C3×C4 |
| Hall | C2×#87639 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8) ⋊ C22×C4 |
232 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72222021, C2×#72222008, #72245767, … |
| maximal normal subgroup of | C2×#72222021, C2×#72222008, #72245767, … |
| maximal quotient of | #72244996, #72245886 |
Past the SmallGroups library coverage — no SmallGroups id.