Finite Group DatabasebetaFinite Group Databasebeta| order | 1452 |
| isoclinism | isoclinic class of D121 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D121 |
| unambiguous semidirect product | C121⋊(C22×C3) |
| unambiguous semidirect product | (C2×C121)⋊(C2×C3) |
| Fitting | C2×C3×C121 ⋊ C2 |
| derived, Sylow | C121 ⋊ C22×C3 |
| Hall | C3×C121 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D121 |
| commutator, cosocle, hypocenter | C121 | C22×C3 |
| Frattini | C11 | C2×C3×D11 |
| Fitting | C2×C3×C121 | C2 |
| socle | C2×C3×C11 | D11 |
| LCS | G ▷ C121 | |
| UCS | C1 ◁ C2×C3 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 726 |
372 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C9×D121, C3×D3×D121, C2×C32×D121, … |
| maximal normal subgroup of | C2×C9×D121, C2×C32×D121, C2×C3×C13×D121, … |
| maximal quotient of | C2×C9×D121, C3×D3×D121, C2×C32×D121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1452, 7);