Finite Group DatabasebetaFinite Group Databasebeta| order | 3528 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×ΓL(1,𝔽8)⋊AGL(1,𝔽7) |
| Fitting, socle | C22×C72 ⋊ C2×C32 |
| derived, Sylow | C72 ⋊ C23×C32 |
| Hall | ΓL(1,𝔽8)2 ⋊ C23 |
| Hall | C22×C7⋊D7 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | ΓL(1,𝔽8)⋊AGL(1,𝔽7) |
| commutator, cosocle, hypocenter | C72 | C23×C32 |
| Frattini | C1 | G |
| Fitting, socle | C22×C72 | C2×C32 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C22 | |
448 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
104 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.