Finite Group DatabasebetaFinite Group Databasebeta| order | 15210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D2535 |
| unambiguous semidirect product | C5⋊(C3⋊D507) |
| unambiguous semidirect product | C169⋊(C3⋊D15) |
| Fitting, derived, Hall | C32×C5×C169 ⋊ C2 |
| Hall | C32×C169 ⋊ D5 |
| Hall | C5×C169 ⋊ C3⋊D3 |
| Sylow | C169 ⋊ C3⋊D15 |
| Hall | C32×C5 ⋊ D169 |
| Sylow | C32 ⋊ D845 |
| Sylow | C5 ⋊ C3⋊D507 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C5×C169 | C2 |
| Frattini | C13 | C3⋊D195 |
| socle | C32×C5×C13 | D13 |
| LCS | G ▷ C32×C5×C169 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7605 |
Polycyclic presentation:
2,3^2,5,13^2|e^13=f^12,b^a=b^2,c^a=c^2,d^a=d^4,e^a=e^12f,f^a=f^123804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊D15×D169, D5×C3⋊D507, C3⋊D3×D845, … |
| maximal normal subgroup of | C3⋊D15×D169, D5×C3⋊D507, C3⋊D3×D845, … |
| maximal quotient of | C3⋊Dic2535, C2×C3⋊D2535 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15210, 32);