Finite Group DatabasebetaFinite Group Databasebeta| order | 2688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#87520 |
| Fitting | C7×#585 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C7 | #1020 |
| commutator, cosocle, hypocenter | #997 | C22×C7 |
| Frattini | C2 | C2×C7×#1020 |
| Fitting | C7×#585 | D3 |
| socle | C2×C7 | C2×#1020 |
| LCS | G ▷ #997 | |
| UCS | C1 ◁ C4×C7 | |
534 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 112 |
182 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)×#87520 |
| maximal normal subgroup of | ΓL(1,𝔽8)×#87520 |
Past the SmallGroups library coverage — no SmallGroups id.