Finite Group DatabasebetaFinite Group Databasebeta| order | 1164 |
| isoclinism | isoclinic class of D3×D97 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D97 |
| unambiguous semidirect product | (D3×C97)⋊C2 |
| unambiguous semidirect product | (C3×D97)⋊C2 |
| unambiguous semidirect product | D291⋊C2 |
| Fitting, socle, derived, Hall | C3×C97 ⋊ C22 |
| Sylow | C97 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×D97 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C97 | C22 |
| LCS | G ▷ C3×C97 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 100 |
| transitive degree | μt(G) = 291 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | D9×D97, D3×D97⋊C3, C3×D3×D97, … |
| maximal normal subgroup of | D3×D97⋊C3, C3×D3×D97, D3×C11×D97, … |
| maximal quotient of | D9×D97, C3×D3×D97, C3⋊D3×D97, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1164, 11);