Finite Group DatabasebetaFinite Group Databasebeta| order | 1452 |
| isoclinism | isoclinic class of D3×D121 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D121 |
| unambiguous semidirect product | (D3×C121)⋊C2 |
| unambiguous semidirect product | (C3×D121)⋊C2 |
| unambiguous semidirect product | D363⋊C2 |
| Fitting, derived, Hall | C3×C121 ⋊ C22 |
| Sylow | C121 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C121 | C22 |
| Frattini | C11 | D3×D11 |
| socle | C3×C11 | C2×D11 |
| LCS | G ▷ C3×C121 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 124 |
| transitive degree | μt(G) = 363 |
186 conjugacy classes — view the full character table.
| maximal subgroup of | D9×D121, C3×D3×D121, C3⋊D3×D121, … |
| maximal normal subgroup of | C3×D3×D121, D3×C13×D121, D3×C17×D121, … |
| maximal quotient of | D9×D121, C3×D3×D121, C3⋊D3×D121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1452, 5);