Finite Group DatabasebetaFinite Group Databasebeta| order | 3528 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×AGL(1,𝔽7)2 |
| Fitting, socle | C2×C72 ⋊ C22×C32 |
| derived, Sylow | C72 ⋊ C23×C32 |
| Hall | ΓL(1,𝔽8)2 ⋊ C23 |
| Hall | C2×D72 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | AGL(1,𝔽7)2 |
| commutator, cosocle, hypocenter | C72 | C23×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72 | C22×C32 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2 | |
394 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
98 conjugacy classes — view the full character table.
| maximal subgroup of | #72222066, D3×AGL(1,𝔽7)2, #72245264, … |
| maximal normal subgroup of | #72222066, #72245264, C4×AGL(1,𝔽7)2, … |
| maximal quotient of | #72222066, D3×AGL(1,𝔽7)2, C2×#72222008, … |
Past the SmallGroups library coverage — no SmallGroups id.