Finite Group DatabasebetaFinite Group Databasebeta| order | 7572 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C22×C631⋊C3 |
| Fitting, socle, Hall | C22×C631 ⋊ C3 |
| derived, Sylow | C631 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C631⋊C3 |
| commutator, hypocenter | C631 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C631 | C3 |
| LCS | G ▷ C631 | |
| UCS | C1 ◁ C22 | |
20 conjugacy classes of subgroups.
852 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊#19150945, A4×C631⋊C3, C22×#19150945, … |
| maximal normal subgroup of | C22⋊#19150945, A4×C631⋊C3, C22×#19150945, … |
| maximal quotient of | C22×#19150943, C2×D3×C631⋊C3, C22×C3×C631⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7572, 12);