Finite Group DatabasebetaFinite Group Databasebeta| order | 9210 |
| automorphism | Aut(G) order 11273040 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4605 |
| unambiguous semidirect product | C3⋊D1535 |
| unambiguous semidirect product | C5⋊D921 |
| unambiguous semidirect product | C307⋊D15 |
| Fitting, socle, derived, Hall | C3×C5×C307 ⋊ C2 |
| Hall | C5×C307 ⋊ D3 |
| Hall | C3×C307 ⋊ D5 |
| Sylow | C307 ⋊ D15 |
| Hall | C3×C5 ⋊ D307 |
| Sylow | C5 ⋊ D921 |
| Sylow | C3 ⋊ D1535 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C307 | C2 |
| LCS | G ▷ C3×C5×C307 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,307|b^a=b^2,c^a=c^4,d^a=d^3062304 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D15×D307, D5×D921, D3×D1535, … |
| maximal normal subgroup of | D15×D307, D5×D921, D3×D1535, … |
| maximal quotient of | Dic4605, C2×D4605, D13815, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9210, 9);