Finite Group DatabasebetaFinite Group Databasebeta| order | 15270 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C509 · Schur multiplier (H2) = C1 |
| direct product | D15×C509 |
| unambiguous semidirect product | C3⋊(D5×C509) |
| unambiguous semidirect product | C5⋊(D3×C509) |
| Fitting, socle, Hall | C3×C5×C509 ⋊ C2 |
| derived, Hall | C3×C5 ⋊ C2×C509 |
| Hall | C5×C509 ⋊ D3 |
| Hall | C3×C509 ⋊ D5 |
| Sylow | C5 ⋊ D3×C509 |
| Sylow | C3 ⋊ D5×C509 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C509 | D15 |
| commutator, cosocle, hypocenter | C3×C5 | C2×C509 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C509 | C2 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C509 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7635 |
4581 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D15×D509, D3×D5×C509, D15⋊D509, … |
| maximal normal subgroup of | D15×D509, D3×D5×C509, D15⋊D509, … |
| maximal quotient of | Dic15×C509, C2×D15×C509 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15270, 7);