Finite Group DatabasebetaFinite Group Databasebeta| order | 2124 |
| isoclinism | isoclinic class of C3⋊D3×D59 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | C3⋊D3×D59 |
| unambiguous semidirect product | (C3×D59)⋊D3 |
| Fitting, socle, derived, Hall | C32×C59 ⋊ C22 |
| Sylow | C59 ⋊ C2×C3⋊D3 |
| Sylow | C32 ⋊ C2×D59 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C59 | C22 |
| LCS | G ▷ C32×C59 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 531 |
186 conjugacy classes — view the full character table.
| maximal subgroup of | C7×C3⋊D3×D59, D59×C3⋊D21, C3⋊D3×D413, … |
| maximal normal subgroup of | C7×C3⋊D3×D59, C11×C3⋊D3×D59, C13×C3⋊D3×D59, … |
| maximal quotient of | C7×C3⋊D3×D59, D59×C3⋊D21, C3⋊D3×D413, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2124, 19);