Finite Group DatabasebetaFinite Group Databasebeta| order | 3528 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | ΓL(1,𝔽8)×C4⋊AGL(1,𝔽7) |
| Fitting | C4×C72 ⋊ C2×C32 |
| Hall | ΓL(1,𝔽8)2 ⋊ D4 |
| Hall | C7×D28 ⋊ C32 |
| Sylow | C72 ⋊ C32×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×ΓL(1,𝔽8)×AGL(1,𝔽7) |
| commutator, socle, cosocle | C2×C72 | C22×C32 |
| Fitting | C4×C72 | C2×C32 |
| hypercenter | C4 | ΓL(1,𝔽8)×AGL(1,𝔽7) |
| hypocenter | C72 | C32×D4 |
| LCS | G ▷ C2×C72 ▷ C72 | |
| UCS | C1 ◁ C2 ◁ C4 | |
198 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
95 conjugacy classes — view the full character table.
| maximal subgroup of | #72245264, ΓL(1,𝔽8)×#1157⋊C3, #72245286, … |
| maximal normal subgroup of | #72245264, ΓL(1,𝔽8)×#1157⋊C3, #72245286, … |
Past the SmallGroups library coverage — no SmallGroups id.