Finite Group DatabasebetaFinite Group Databasebeta| order | 15246 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C112 · Schur multiplier (H2) = C3×C11 |
| direct product | C7×C112×C3⋊D3 |
| unambiguous semidirect product | C3⋊(D3×C7×C112) |
| Fitting, socle, Hall | C32×C7×C112 ⋊ C2 |
| derived, Sylow | C32 ⋊ C2×C7×C112 |
| Hall | C32×C112 ⋊ C2×C7 |
| Hall | C32×C7 ⋊ C2×C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C112 | C3⋊D3 |
| commutator, cosocle, hypocenter | C32 | C2×C7×C112 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C112 | C2 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C7×C112 | |
336 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7623 |
5082 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×C112×#157, C7×C11×C11⋊#157, C7×C11⋊(C11⋊#157), … |
| maximal normal subgroup of | C7×C112×#157, C7×C11×C11⋊#157, C7×C11⋊(C11⋊#157), … |
| maximal quotient of | C7×C112×C3⋊Dic3, C2×C7×C112×C3⋊D3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15246, 105);