Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C34 |
| direct product | C9×C32⋊(C19⋊C3) |
| Fitting | C32×C9×C19 ⋊ C3 |
| Sylow | C19 ⋊ C9×H(3,𝔽3) |
202 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1539 |
585 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28353152, #28353154, #28353169, … |
| maximal normal subgroup of | #28353152, #28353154, #28353169, … |
| maximal quotient of | C9×C32⋊#4294, C9×#13095303, #28353529, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 168);