Finite Group DatabasebetaFinite Group Databasebeta| order | 2124 |
| isoclinism | isoclinic class of C59⋊#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C59⋊#157 |
| Fitting, socle, derived, Hall | C32×C59 ⋊ C4 |
| Sylow | C59 ⋊ #157 |
| Sylow | C32 ⋊ Dic59 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C59 | C4 |
| prime radical, cosocle | C3⋊D3×C59 | C2 |
| LCS | G ▷ C32×C59 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 354 |
Polycyclic presentation:
2^2,3^2,59|a^2=b,c^a=cd,d^a=cd^2,e^a=e^58,c^b=c^2,d^b=d^2180 conjugacy classes — view the full character table.
| maximal subgroup of | C7×C59⋊#157, C7⋊(C59⋊#157), C11×C59⋊#157, … |
| maximal normal subgroup of | C7×C59⋊#157, C11×C59⋊#157, C13×C59⋊#157, … |
| maximal quotient of | C7×C59⋊#157, C7⋊(C59⋊#157), C11×C59⋊#157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2124, 24);