Finite Group DatabasebetaFinite Group Databasebeta| order | 22710 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D757⋊C3 |
| unambiguous semidirect product | D757⋊(C3×C5) |
| unambiguous semidirect product | (C757⋊C3)⋊(C2×C5) |
| unambiguous semidirect product | (C5×D757)⋊C3 |
| Fitting, socle, Hall | C5×C757 ⋊ C2×C3 |
| derived, Sylow | C757 ⋊ C2×C3×C5 |
| Hall | C5×C757⋊C3 ⋊ C2 |
| Hall | C5×D757 ⋊ C3 |
| Hall | C757⋊C3 ⋊ C2×C5 |
| Hall | D757 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D757⋊C3 |
| commutator, cosocle, hypocenter | C757 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C757 | C2×C3 |
| LCS | G ▷ C757 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3785 |
660 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22710, 10);