Finite Group DatabasebetaFinite Group Databasebeta| order | 15210 |
| isoclinism | isoclinic class of C13⋊D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3×C13 |
| direct product | C32×C5×C13⋊D13 |
| Fitting, socle, Hall | C32×C5×C132 ⋊ C2 |
| derived, Sylow | C132 ⋊ C2×C32×C5 |
| Hall | C32×C132 ⋊ C2×C5 |
| Hall | C5×C132 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C5 | C13⋊D13 |
| commutator, cosocle, hypocenter | C132 | C2×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C132 | C2 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C32×C5 | |
384 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7605 |
3870 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C5×D132, C32×C5×#10621729, C32×C5×#10621728, … |
| maximal normal subgroup of | C32×C5×D132, C32×C5×#10621729, C32×C5×#10621728, … |
| maximal quotient of | C32×C5×#10621725, C2×C32×C5×C13⋊D13 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15210, 135);