Finite Group DatabasebetaFinite Group Databasebeta| order | 7130 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊(D31⋊C5) |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊D23 |
| unambiguous semidirect product | D713⋊C5 |
| Fitting, socle, derived, Hall | C23×C31 ⋊ C2×C5 |
| Hall | C23×ΓL(1,𝔽32) ⋊ C2 |
| Hall | D713 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ D23 |
| Sylow | C31 ⋊ C5×D23 |
| Sylow | C23 ⋊ D31⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C23×C31 | C2×C5 |
| LCS | G ▷ C23×C31 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,23,31|c^a=c^22,d^a=d^30,d^b=d^16134 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7130, 12);