Finite Group DatabasebetaFinite Group Databasebeta| order | 3528 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×C3×#64423 |
| Fitting, socle | C22×C3×C72 ⋊ C2×C3 |
| derived, Sylow | C72 ⋊ C23×C32 |
| Hall | C3×#3861 ⋊ C23 |
| Hall | C22×C7×D7 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #64423 |
| commutator, cosocle, hypocenter | C72 | C23×C32 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C72 | C2×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C22×C3 | |
474 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 148 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
204 conjugacy classes — view the full character table.
| maximal subgroup of | C22×C3×#64423⋊C2, C22×D3×#64423, C22×#64423⋊D3, … |
| maximal normal subgroup of | C22×C3×#64423⋊C2, C22×D3×#64423, C22×#64423⋊D3, … |
| maximal quotient of | C2×C3×#11924207 |
Past the SmallGroups library coverage — no SmallGroups id.