Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of C3⋊D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3⋊(C9⋊C8) |
| unambiguous semidirect product | (C2×C3)⋊(C9⋊C8) |
| unambiguous semidirect product | (C2×C9)⋊(C3⋊C8) |
| derived, Sylow | C3×C9 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | C3⋊D9 |
| commutator, hypocenter | C3×C9 | C2×C8 |
| Frattini | C3×C4 | C2×C3⋊D3 |
| Fitting | C2×C3×C4×C9 | C2 |
| socle, prime radical | C22×C32 | Dic3 |
| cosocle | C3×C4×C9 | C22 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C2×C4 | |
110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 432 |
A minimal faithful permutation representation — 3 generators on 22 points:
(1,2)(4,5)(6,7,8,10,9,11,12,13)(15,17)(16,20)(18,19)(21,22);(1,2)(3,4,5);(14,22,17,20,19,18,16,15,21)120 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×C9⋊C8, #11720258, Dic3⋊(C9⋊C8), … |
| maximal normal subgroup of | Dic3×C9⋊C8, #11720258, Dic3⋊(C9⋊C8), … |
| maximal quotient of | C4×C3⋊(C9⋊C8), C4⋊(C3⋊(C9⋊C8)), C2×C3⋊(C9⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 178);