Finite Group DatabasebetaFinite Group Databasebeta| order | 16330 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊(D71⋊C5) |
| unambiguous semidirect product | (C71⋊C5)⋊D23 |
| unambiguous semidirect product | D1633⋊C5 |
| Fitting, socle, derived, Hall | C23×C71 ⋊ C2×C5 |
| Hall | C23×C71⋊C5 ⋊ C2 |
| Hall | D1633 ⋊ C5 |
| Hall | C71⋊C5 ⋊ D23 |
| Sylow | C71 ⋊ C5×D23 |
| Sylow | C23 ⋊ D71⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C71 | C2×C5 |
| LCS | G ▷ C23×C71 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1633 |
Polycyclic presentation:
2,5,23,71|c^a=c^22,d^a=d^70,d^b=d^54226 conjugacy classes — view the full character table.
| maximal subgroup of | D23×D71⋊C5, C2×C23⋊(D71⋊C5) |
| maximal normal subgroup of | D23×D71⋊C5, C2×C23⋊(D71⋊C5) |
| maximal quotient of | C23⋊(Dic71⋊C5), C2×C23⋊(D71⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16330, 12);