Finite Group DatabasebetaFinite Group Databasebeta| order | 23170 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(D331⋊C5) |
| unambiguous semidirect product | (C331⋊C5)⋊D7 |
| unambiguous semidirect product | D2317⋊C5 |
| Fitting, socle, derived, Hall | C7×C331 ⋊ C2×C5 |
| Hall | C7×C331⋊C5 ⋊ C2 |
| Hall | D2317 ⋊ C5 |
| Hall | C331⋊C5 ⋊ D7 |
| Sylow | C331 ⋊ C5×D7 |
| Sylow | C7 ⋊ D331⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C331 | C2×C5 |
| LCS | G ▷ C7×C331 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2317 |
Polycyclic presentation:
2,5,7,331|c^a=c^6,d^a=d^330,d^b=d^64256 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23170, 12);