Finite Group DatabasebetaFinite Group Databasebeta| order | 14112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | ΓL(1,𝔽8)2×#99 |
| Fitting, Hall | C72×#99 ⋊ C32 |
| Sylow | C72 ⋊ C32×#99 |
728 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
275 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #99×ΓL(1,𝔽8)⋊AGL(1,𝔽7), ΓL(1,𝔽8)2×B(4,𝔽2), #72254299 |
| maximal normal subgroup of | #99×ΓL(1,𝔽8)⋊AGL(1,𝔽7), ΓL(1,𝔽8)2×B(4,𝔽2), #72254299 |
Past the SmallGroups library coverage — no SmallGroups id.