Finite Group DatabasebetaFinite Group Databasebeta| order | 8730 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D1455 |
| unambiguous semidirect product | C5⋊(C3⋊D291) |
| unambiguous semidirect product | C97⋊(C3⋊D15) |
| Fitting, socle, derived, Hall | C32×C5×C97 ⋊ C2 |
| Hall | C32×C97 ⋊ D5 |
| Hall | C5×C97 ⋊ C3⋊D3 |
| Sylow | C97 ⋊ C3⋊D15 |
| Hall | C32×C5 ⋊ D97 |
| Sylow | C32 ⋊ D485 |
| Sylow | C5 ⋊ C3⋊D291 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C5×C97 | C2 |
| LCS | G ▷ C32×C5×C97 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,5,97|b^a=b^2,c^a=c^2,d^a=d^4,e^a=e^962184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊D15×D97, D5×C3⋊D291, C3⋊D3×D485, … |
| maximal normal subgroup of | C3⋊D15×D97, D5×C3⋊D291, C3⋊D3×D485, … |
| maximal quotient of | C3⋊Dic1455, C2×C3⋊D1455 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8730, 32);