Finite Group DatabasebetaFinite Group Databasebeta| order | 15618 |
| isoclinism | isoclinic class of C19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C137 · Schur multiplier (H2) = C1 |
| direct product | C2×C19⋊C3×C137 |
| unambiguous semidirect product | (C2×C19)⋊(C3×C137) |
| unambiguous semidirect product | (C2×C19×C137)⋊C3 |
| Fitting, socle, Hall | C2×C19×C137 ⋊ C3 |
| derived, Sylow | C19 ⋊ C2×C3×C137 |
| Hall | C19×C137 ⋊ C2×C3 |
| Hall | C2×C19 ⋊ C3×C137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C137 | C19⋊C3 |
| commutator, cosocle, hypocenter | C19 | C2×C3×C137 |
| Frattini | C1 | G |
| Fitting, socle | C2×C19×C137 | C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C2×C137 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5206 |
2466 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C19⋊C3×C137, C19⋊C3×Dic137, C137×(C19⋊C3)⋊C4, … |
| maximal normal subgroup of | C4×C19⋊C3×C137, C19⋊C3×Dic137, C137×(C19⋊C3)⋊C4, … |
| maximal quotient of | C4×C19⋊C3×C137, C22×C19⋊C3×C137 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15618, 2);