Finite Group DatabasebetaFinite Group Databasebeta| order | 15210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| Fitting | C3×C5×C169 ⋊ C2×C3 |
| derived, Hall | C5×C169 ⋊ C2×C32 |
| Hall | C3×C5×C169⋊C3 ⋊ C2 |
| Hall | D845 ⋊ C32 |
| Hall | C3×C169⋊C3 ⋊ D5 |
| Sylow | C169 ⋊ C32×D5 |
| Sylow | C5 ⋊ C3×D169⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C5⋊(D169⋊C3) |
| commutator, cosocle, hypocenter | C5×C169 | C2×C32 |
| Frattini | C13 | C3×C5⋊(D13⋊C3) |
| Fitting | C3×C5×C169 | C2×C3 |
| socle | C3×C5×C13 | D13⋊C3 |
| LCS | G ▷ C5×C169 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2535 |
456 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#16809981⋊C3, C3×#16809980⋊C3, C3×D5×D169⋊C3, … |
| maximal normal subgroup of | C3×#16809981⋊C3, C3×#16809980⋊C3, C3×D5×D169⋊C3, … |
| maximal quotient of | C3×Dic845⋊C3, C2×C3×C5⋊(D169⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15210, 16);