Finite Group DatabasebetaFinite Group Databasebeta| order | 2124 |
| isoclinism | isoclinic class of C3⋊D177 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊Dic177 |
| unambiguous semidirect product | C59⋊(C3⋊Dic3) |
| derived, Hall | C32×C59 ⋊ C4 |
| Sylow | C59 ⋊ C3⋊Dic3 |
| Sylow | C32 ⋊ Dic59 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊D177 |
| commutator, hypocenter | C32×C59 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C32×C59 | C2 |
| LCS | G ▷ C32×C59 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2124 |
Polycyclic presentation:
2,3^2,59,2|a^2=e,b^a=b^2,c^a=c^2,d^a=d^58534 conjugacy classes — view the full character table.
| maximal subgroup of | C7×C3⋊Dic177, C3⋊Dic1239, C3⋊Dic1947, … |
| maximal normal subgroup of | C7×C3⋊Dic177, C11×C3⋊Dic177, C13×C3⋊Dic177, … |
| maximal quotient of | C7×C3⋊Dic177, C3⋊Dic1239, C3⋊Dic1947, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2124, 16);