Finite Group DatabasebetaFinite Group Databasebeta| order | 15210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#15690146 |
| derived, Hall | #13095201 ⋊ C2×C5 |
| Hall | C5×#13095201 ⋊ C2 |
| Hall | C5×C132 ⋊ D9 |
| Sylow | C132 ⋊ C5×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #15690146 |
| commutator, cosocle, hypocenter | #13095201 | C2×C5 |
| Frattini | C3 | C5×#11759813 |
| Fitting, socle | C3×C5×C132 | D3 |
| LCS | G ▷ #13095201 | |
| UCS | C1 ◁ C5 | |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 585 |
540 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#15690146⋊C2, #15690146⋊D5, D5×#15690146, … |
| maximal normal subgroup of | C5×#15690146⋊C2, #15690146⋊D5, D5×#15690146, … |
| maximal quotient of | C5×#20258750, C2×C5×#15690146 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15210, 41);