Finite Group DatabasebetaFinite Group Databasebeta| order | 22170 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C2×C5×C739⋊C3 |
| unambiguous semidirect product | (C2×C739)⋊(C3×C5) |
| unambiguous semidirect product | (C2×C5×C739)⋊C3 |
| Fitting, socle, Hall | C2×C5×C739 ⋊ C3 |
| derived, Sylow | C739 ⋊ C2×C3×C5 |
| Hall | C5×C739 ⋊ C2×C3 |
| Hall | C2×C739 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C739⋊C3 |
| commutator, cosocle, hypocenter | C739 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C739 | C3 |
| LCS | G ▷ C739 | |
| UCS | C1 ◁ C2×C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7390 |
2490 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22170, 2);