Finite Group DatabasebetaFinite Group Databasebeta| order | 4568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C22×D571 |
| unambiguous semidirect product | C571⋊C23 |
| unambiguous semidirect product | (C2×C571)⋊C22 |
| Fitting, socle | C22×C571 ⋊ C2 |
| derived, Sylow | C571 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D571 |
| commutator, cosocle, hypocenter | C571 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C22×C571 | C2 |
| LCS | G ▷ C571 | |
| UCS | C1 ◁ C22 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2284 |
1148 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4568, 12);