Finite Group DatabasebetaFinite Group Databasebeta| order | 3528 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C7 |
| direct product | D32×C7⋊D7 |
| Fitting, socle, derived, Hall | C32×C72 ⋊ C23 |
| Sylow | C72 ⋊ C2×D32 |
| Sylow | C32 ⋊ C22×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C72 | C23 |
| LCS | G ▷ C32×C72 | |
| UCS | C1 | |
690 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 690 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.
234 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#64424, D32×D72, D32×ΓL(1,𝔽8)⋊D7, … |
| maximal normal subgroup of | D32×#64424, D32×D72, D32×ΓL(1,𝔽8)⋊D7, … |
| maximal quotient of | D3×C3⋊D3×C7⋊D7 |
Past the SmallGroups library coverage — no SmallGroups id.