Finite Group DatabasebetaFinite Group Databasebeta| order | 4572 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C4×#11765919 |
| Fitting, Hall | C4×C127 ⋊ C9 |
| derived, Sylow | C127 ⋊ C4×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #11765919 |
| commutator, hypocenter | C127 | C4×C9 |
| Frattini | C2 | C2×#11765919 |
| Fitting | C4×C127 | C9 |
| socle | C2×C127 | C2×C9 |
| prime radical, cosocle | C2×C127⋊C3 | C2×C3 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C4 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 131 |
| transitive degree | μt(G) = 508 |
92 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4572, 18);