Finite Group DatabasebetaFinite Group Databasebeta| order | 2124 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C59 · Schur multiplier (H2) = C2 |
| direct product | C2×D9×C59 |
| unambiguous semidirect product | C9⋊(C22×C59) |
| unambiguous semidirect product | (C2×C9)⋊(C2×C59) |
| Fitting | C2×C9×C59 ⋊ C2 |
| derived, Sylow | C9 ⋊ C22×C59 |
| Hall | C9×C59 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C59 | D9 |
| commutator, cosocle, hypocenter | C9 | C22×C59 |
| Frattini | C3 | C2×D3×C59 |
| Fitting | C2×C9×C59 | C2 |
| socle | C2×C3×C59 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C2×C59 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1062 |
708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×D9×C59, C2×C7×D9×C59, C2×C59×D63, … |
| maximal normal subgroup of | C2×C7×D9×C59, C2×C11×D9×C59, C2×C13×D9×C59, … |
| maximal quotient of | D7×D9×C59, C2×C7×D9×C59, C2×C59×D63, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2124, 9);