Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #634⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | C4⋊((C3⋊Dic3)⋊C3) |
| unambiguous semidirect product | (C4⋊(C3⋊Dic3))⋊C3 |
| Sylow | H(3,𝔽3) ⋊ C4⋊C4 |
107 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 2 generators on 17 points:
(5,6,7,8)(9,10,16)(11,13,15)(12,14,17);(1,2,3,4)(6,8)(10,12)(11,14)(13,15)(16,17)Polycyclic presentation:
2^2,3,2^2,3^2|a^2=d,b^2=e,b^a=be,f^a=f^2,g^a=g^2,f^c=fg62 conjugacy classes — view the full character table.
| maximal subgroup of | #11720306, #11720307, #11720313, … |
| maximal normal subgroup of | #11720306, #11720307, #11720313, … |
| maximal quotient of | C4⋊((C3⋊(C3⋊C8))⋊C3), #63646⋊C3, #63644⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 140);