Finite Group DatabasebetaFinite Group Databasebeta| order | 2124 |
| isoclinism | isoclinic class of D59 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C9×D59 |
| unambiguous semidirect product | C59⋊(C22×C9) |
| unambiguous semidirect product | (C2×C59)⋊(C2×C9) |
| Fitting | C2×C9×C59 ⋊ C2 |
| derived, Sylow | C59 ⋊ C22×C9 |
| Hall | C9×C59 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | D59 |
| commutator, hypocenter | C59 | C22×C9 |
| Frattini | C3 | C2×C3×D59 |
| Fitting | C2×C9×C59 | C2 |
| socle | C2×C3×C59 | C2×C3 |
| prime radical | C2×C3×D59 | C3 |
| cosocle | C3×C59 | C22×C3 |
| LCS | G ▷ C59 | |
| UCS | C1 ◁ C2×C9 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1062 |
558 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×D7⋊C9, C2×C59⋊(D7⋊C9), C2×C7⋊C9×D59, … |
| maximal normal subgroup of | C2×C7×C9×D59, C2×C9×C11×D59, C2×C9×C13×D59, … |
| maximal quotient of | D59×D7⋊C9, C2×C59⋊(D7⋊C9), C2×C7⋊C9×D59, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2124, 8);