Finite Group DatabasebetaFinite Group Databasebeta| order | 1413 |
| isoclinism | isoclinic class of C157⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×C157⋊C3 |
| unambiguous semidirect product | C157⋊C32 |
| unambiguous semidirect product | (C3×C157)⋊C3 |
| Fitting, socle | C3×C157 ⋊ C3 |
| derived, Sylow | C157 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C157⋊C3 |
| commutator, cosocle, hypocenter | C157 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C157 | C3 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 471 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D157⋊C3, C3⋊(D157⋊C3), D3×C157⋊C3, … |
| maximal normal subgroup of | C3×D157⋊C3, C3⋊(D157⋊C3), D3×C157⋊C3, … |
| maximal quotient of | C2×C3×C157⋊C3, C9×C157⋊C3, C3×C157⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1413, 3);