Finite Group DatabasebetaFinite Group Databasebeta| order | 4557 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C31×C49 ⋊ C3 |
| Sylow | C49 ⋊ C31⋊C3 |
| Sylow | C31 ⋊ C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C31×C49 | C3 |
| Frattini | C7 | #10620252 |
| socle | C7×C31 | ΓL(1,𝔽8) |
| LCS | G ▷ C31×C49 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 80 |
| transitive degree | μt(G) = 1519 |
Polycyclic presentation:
3,7,31,7|b^7=d^2,b^a=b^2d,c^a=c^5,d^a=d^2509 conjugacy classes — view the full character table.
| maximal subgroup of | C31⋊C3×C49⋊C3, C3×#17986945, C22⋊#17986945, … |
| maximal normal subgroup of | C31⋊C3×C49⋊C3, C3×#17986945, C5×#17986945, … |
| maximal quotient of | #28331763, C3×#17986945, C22⋊#17986945, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4557, 4);