Finite Group DatabasebetaFinite Group Databasebeta| order | 4572 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×(C127⋊C3)⋊C4 |
| unambiguous semidirect product | (C127⋊C3)⋊(C3×C4) |
| unambiguous semidirect product | Dic127⋊C32 |
| unambiguous semidirect product | (C3×Dic127)⋊C3 |
| derived, Sylow | C127 ⋊ C32×C4 |
| Hall | C3×C127⋊C3 ⋊ C4 |
| Hall | Dic127 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D127⋊C3 |
| commutator, hypocenter | C127 | C32×C4 |
| Frattini | C2 | C3×D127⋊C3 |
| Fitting, socle | C2×C3×C127 | C2×C3 |
| prime radical | C2×C3×C127⋊C3 | C2 |
| cosocle | C2×C127 | C2×C32 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1524 |
162 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4572, 19);