Finite Group DatabasebetaFinite Group Databasebeta| order | 3528 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C3 |
| direct product | ΓL(1,𝔽8)×ΓL(1,𝔽8)⋊Q8 |
| Hall | ΓL(1,𝔽8)2 ⋊ Q8 |
| Hall | C7×Dic14 ⋊ C32 |
| Sylow | C72 ⋊ C32×Q8 |
150 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
95 conjugacy classes — view the full character table.
| maximal subgroup of | #72245242, ΓL(1,𝔽8)×#1157⋊C3, #72245286, … |
| maximal normal subgroup of | #72245242, ΓL(1,𝔽8)×#1157⋊C3, #72245286, … |
Past the SmallGroups library coverage — no SmallGroups id.