Finite Group DatabasebetaFinite Group Databasebeta| order | 15730 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C13 · Schur multiplier (H2) = C1 |
| direct product | C2×C13×#10597243 |
| Fitting, socle, Hall | C2×C112×C13 ⋊ C5 |
| derived, Sylow | C112 ⋊ C2×C5×C13 |
| Hall | C112×C13 ⋊ C2×C5 |
| Hall | C2×C112 ⋊ C5×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | #10597243 |
| commutator, cosocle, hypocenter | C112 | C2×C5×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C112×C13 | C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C2×C13 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3146 |
754 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×#14559051, #44538112, C13×#14559054, … |
| maximal normal subgroup of | C13×#14559051, #44538112, C13×#14559054, … |
| maximal quotient of | C4×C13×#10597243, C22×C13×#10597243 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15730, 40);