Finite Group DatabasebetaFinite Group Databasebeta| order | 3528 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×ΓL(1,𝔽8)×ΓL(1,𝔽8)⋊C4 |
| derived, Sylow | C72 ⋊ C2×C32×C4 |
| Hall | ΓL(1,𝔽8)2 ⋊ C2×C4 |
| Hall | C2×C7×Dic7 ⋊ C32 |
202 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 79 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×#72222008, C2×ΓL(1,𝔽8)×(C22⋊D7)⋊C3, C2×#72222015, … |
| maximal normal subgroup of | C2×#72222008, C2×ΓL(1,𝔽8)×(C22⋊D7)⋊C3, C2×#72222015, … |
| maximal quotient of | ΓL(1,𝔽8)×#1136⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.