Finite Group DatabasebetaFinite Group Databasebeta| order | 15270 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C509 · Schur multiplier (H2) = C1 |
| direct product | C3×D5×C509 |
| unambiguous semidirect product | C5⋊(C2×C3×C509) |
| Fitting, socle, Hall | C3×C5×C509 ⋊ C2 |
| derived, Sylow | C5 ⋊ C2×C3×C509 |
| Hall | C5×C509 ⋊ C2×C3 |
| Hall | C3×C5 ⋊ C2×C509 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C509 | D5 |
| commutator, cosocle, hypocenter | C5 | C2×C3×C509 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C509 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C3×C509 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7635 |
6108 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×AGL(1,𝔽5)×C509, C3×#23779147, C3×D5×D509, … |
| maximal normal subgroup of | C3×AGL(1,𝔽5)×C509, C3×#23779147, C3×D5×D509, … |
| maximal quotient of | C3×Dic5×C509, C2×C3×D5×C509 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15270, 3);