Finite Group DatabasebetaFinite Group Databasebeta| order | 7572 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C631⋊C3)⋊C4 |
| unambiguous semidirect product | Dic631⋊C3 |
| derived, Sylow | C631 ⋊ C3×C4 |
| Hall | Dic631 ⋊ C3 |
| Hall | C631⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D631⋊C3 |
| commutator, hypocenter | C631 | C3×C4 |
| Fitting, socle | C2×C631 | C2×C3 |
| LCS | G ▷ C631 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,631,2|a^2=d,c^a=c^630,c^b=c^587222 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7572, 2);