Finite Group DatabasebetaFinite Group Databasebeta| order | 5292 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32 |
| direct product | C2×#72224656 |
| Hall | (C3×ΓL(1,𝔽8))⋊ΓL(1,𝔽8) ⋊ C22 |
| Hall | C2×C7⋊D7 ⋊ H(3,𝔽3) |
| Sylow | C72 ⋊ C22×H(3,𝔽3) |
280 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 126 |
92 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72224660 |
| maximal normal subgroup of | C2×#72224660 |
Past the SmallGroups library coverage — no SmallGroups id.