Finite Group DatabasebetaFinite Group Databasebeta| order | 22575 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C52⋊((C43⋊C3)⋊C7) |
| unambiguous semidirect product | (C43⋊C7)⋊(C52⋊C3) |
| unambiguous semidirect product | (C52⋊(C43⋊C3))⋊C7 |
| Fitting, socle, derived, Hall | C52×C43 ⋊ C3×C7 |
| Hall | C52×C43⋊C7 ⋊ C3 |
| Hall | C52⋊(C43⋊C3) ⋊ C7 |
| Hall | C43⋊C7 ⋊ C52⋊C3 |
| Sylow | C43 ⋊ C7×C52⋊C3 |
| Sylow | C52 ⋊ (C43⋊C3)⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C43 | C3×C7 |
| LCS | G ▷ C52×C43 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 645 |
Polycyclic presentation:
3,7,5^2,43|c^a=cd^2,d^a=cd^3,e^a=e^36,e^b=e^41127 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22575, 9);