Finite Group DatabasebetaFinite Group Databasebeta| order | 4572 |
| automorphism | Aut(G) order 1728216 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2286 |
| direct product | C2×D1143 |
| unambiguous semidirect product | (C2×C9)⋊D127 |
| unambiguous semidirect product | (C2×C127)⋊D9 |
| Fitting | C2×C9×C127 ⋊ C2 |
| derived, Hall | C9×C127 ⋊ C22 |
| Sylow | C127 ⋊ C2×D9 |
| Sylow | C9 ⋊ C2×D127 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1143 |
| commutator, cosocle, hypocenter | C9×C127 | C22 |
| Frattini | C3 | C2×D381 |
| Fitting | C2×C9×C127 | C2 |
| socle | C2×C3×C127 | D3 |
| LCS | G ▷ C9×C127 | |
| UCS | C1 ◁ C2 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2286 |
1146 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×D1143, C2×D5715, C2×C5×D1143, … |
| maximal normal subgroup of | C2×C5×D1143, C2×C9⋊(D127⋊C7), C2×C7×D1143, … |
| maximal quotient of | D5×D1143, C2×D5715, C2×C5×D1143, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4572, 15);