Finite Group DatabasebetaFinite Group Databasebeta| order | 9210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(D307⋊C3) |
| unambiguous semidirect product | (C307⋊C3)⋊D5 |
| unambiguous semidirect product | D1535⋊C3 |
| Fitting, socle, derived, Hall | C5×C307 ⋊ C2×C3 |
| Hall | C5×C307⋊C3 ⋊ C2 |
| Hall | D1535 ⋊ C3 |
| Hall | C307⋊C3 ⋊ D5 |
| Sylow | C307 ⋊ C3×D5 |
| Sylow | C5 ⋊ D307⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C307 | C2×C3 |
| LCS | G ▷ C5×C307 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,307|c^a=c^4,d^a=d^306,d^b=d^289267 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9210, 12);