Finite Group DatabasebetaFinite Group Databasebeta| order | 15050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D1505 |
| unambiguous semidirect product | C5⋊(C5×D301) |
| unambiguous semidirect product | C7⋊(C5×D215) |
| unambiguous semidirect product | C43⋊(C5×D35) |
| Fitting, socle, Hall | C52×C7×C43 ⋊ C2 |
| derived | C5×C7×C43 ⋊ C2×C5 |
| Hall | C52×C43 ⋊ D7 |
| Hall | C7×C43 ⋊ C5×D5 |
| Hall | C52×C7 ⋊ D43 |
| Sylow | C43 ⋊ C5×D35 |
| Sylow | C52 ⋊ D301 |
| Sylow | C7 ⋊ C5×D215 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D1505 |
| commutator, cosocle, hypocenter | C5×C7×C43 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C43 | C2 |
| LCS | G ▷ C5×C7×C43 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3010 |
3770 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D35×D43, C5×D7×D215, C5×D5×D301, … |
| maximal normal subgroup of | C5×D35×D43, C5×D7×D215, C5×D5×D301, … |
| maximal quotient of | C5×Dic1505, C2×C5×D1505 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15050, 24);