Finite Group DatabasebetaFinite Group Databasebeta| order | 15730 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C112 · Schur multiplier (H2) = C11 |
| direct product | C5×C112×D13 |
| unambiguous semidirect product | C13⋊(C2×C5×C112) |
| Fitting, socle, Hall | C5×C112×C13 ⋊ C2 |
| derived, Sylow | C13 ⋊ C2×C5×C112 |
| Hall | C112×C13 ⋊ C2×C5 |
| Hall | C5×C13 ⋊ C2×C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C112 | D13 |
| commutator, cosocle, hypocenter | C13 | C2×C5×C112 |
| Frattini | C1 | G |
| Fitting, socle | C5×C112×C13 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C5×C112 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7865 |
4840 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C112×#261, C5×C11×C11⋊#261, C5×C11×D11×D13, … |
| maximal normal subgroup of | C5×C112×#261, C5×C11×C11⋊#261, C5×C11×D11×D13, … |
| maximal quotient of | C5×C112×Dic13, C2×C5×C112×D13 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15730, 54);