Finite Group DatabasebetaFinite Group Databasebeta| order | 14112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C22×C3×C4 |
| direct product | ΓL(1,𝔽8)2×#127 |
| Fitting, Hall | C72×#127 ⋊ C32 |
| Sylow | C72 ⋊ C32×#127 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×ΓL(1,𝔽8)2 |
| commutator, socle, cosocle | C22×C72 | C23×C32 |
| Fitting | C72×#127 | C32 |
| hypercenter | #127 | ΓL(1,𝔽8)2 |
| hypocenter | C72 | C32×#127 |
| LCS | G ▷ C22×C72 ▷ C72 | |
| UCS | C1 ◁ C22 ◁ #127 | |
1512 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 1512 conjugacy classes of subgroups — too many to draw. Only its 286 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
350 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #127×ΓL(1,𝔽8)⋊AGL(1,𝔽7), ΓL(1,𝔽8)2×#453, #72246406 |
| maximal normal subgroup of | #127×ΓL(1,𝔽8)⋊AGL(1,𝔽7), ΓL(1,𝔽8)2×#453, #72246406 |
Past the SmallGroups library coverage — no SmallGroups id.