Finite Group DatabasebetaFinite Group Databasebeta| order | 4557 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C31 ⋊ C3 |
| Sylow | C72 ⋊ C31⋊C3 |
| Sylow | C31 ⋊ #3861 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C31 | C3 |
| LCS | G ▷ C72×C31 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1519 |
Polycyclic presentation:
3,7^2,31|b^a=b^2,c^a=c^2,d^a=d^5509 conjugacy classes — view the full character table.
| maximal subgroup of | C31⋊C3×#3861, ΓL(1,𝔽8)×#10620252, #28331790, … |
| maximal normal subgroup of | C31⋊C3×#3861, ΓL(1,𝔽8)×#10620252, #28331790, … |
| maximal quotient of | #28331777, C3×#17986953, C22⋊#17986953, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4557, 12);