Finite Group DatabasebetaFinite Group Databasebeta| order | 23170 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D331⋊C5 |
| unambiguous semidirect product | D331⋊(C5×C7) |
| unambiguous semidirect product | (C331⋊C5)⋊(C2×C7) |
| unambiguous semidirect product | (C7×D331)⋊C5 |
| Fitting, socle, Hall | C7×C331 ⋊ C2×C5 |
| derived, Sylow | C331 ⋊ C2×C5×C7 |
| Hall | C7×C331⋊C5 ⋊ C2 |
| Hall | C7×D331 ⋊ C5 |
| Hall | C331⋊C5 ⋊ C2×C7 |
| Hall | D331 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D331⋊C5 |
| commutator, cosocle, hypocenter | C331 | C2×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C331 | C2×C5 |
| LCS | G ▷ C331 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2317 |
301 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23170, 10);