Finite Group DatabasebetaFinite Group Databasebeta| order | 22085 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C631⋊C5)⋊C7 |
| unambiguous semidirect product | (C631⋊C7)⋊C5 |
| Fitting, socle, derived, Sylow | C631 ⋊ C5×C7 |
| Hall | C631⋊C7 ⋊ C5 |
| Hall | C631⋊C5 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C631 | C5×C7 |
| LCS | G ▷ C631 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 631 |
Polycyclic presentation:
5,7,631|c^a=c^242,c^b=c^26953 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22085, 1);