Finite Group DatabasebetaFinite Group Databasebeta| order | 22265 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C73 · Schur multiplier (H2) = C1 |
| direct product | C73×C61⋊C5 |
| unambiguous semidirect product | C61⋊(C5×C73) |
| unambiguous semidirect product | (C61×C73)⋊C5 |
| Fitting, socle, Hall | C61×C73 ⋊ C5 |
| derived, Sylow | C61 ⋊ C5×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C73 | C61⋊C5 |
| commutator, cosocle, hypocenter | C61 | C5×C73 |
| Frattini | C1 | G |
| Fitting, socle | C61×C73 | C5 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C73 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4453 |
1241 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22265, 1);