Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| isoclinism | isoclinic class of C19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C35 · Schur multiplier (H2) = C310 |
| direct product | C34×C19⋊C3 |
| unambiguous semidirect product | C19⋊C35 |
| unambiguous semidirect product | (C3×C19)⋊C34 |
| Fitting, socle | C34×C19 ⋊ C3 |
| derived, Sylow | C19 ⋊ C35 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C34 | C19⋊C3 |
| commutator, cosocle, hypocenter | C19 | C35 |
| Frattini | C1 | G |
| Fitting, socle | C34×C19 | C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C34 | |
5328 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1539 |
729 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28353504, C19⋊C3×#6866, C3×#17987334, … |
| maximal normal subgroup of | #28353504, C19⋊C3×#6866, C3×#17987334, … |
| maximal quotient of | C33×C9×C19⋊C3, C34×#4294, C32×H(3,𝔽3)×C19⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 309);