Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #88627 |
| automorphism | Aut(G) = D4×AΓL(1,𝔽9) (order 1152) · Inn(G) = C2×#157 · Out(G) = C2×D4 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#1088 |
| Fitting | C4×H(3,𝔽3) ⋊ C4 |
| Sylow | H(3,𝔽3) ⋊ C4⋊C4 |
71 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 2 generators on 22 points:
(1,3,16)(2,15,6)(4,12,9)(5,10,18)(7,17,11)(8,13,14)(19,20,21,22);(1,2)(3,7,9,14)(4,11)(5,8)(6,12,13,18)(10,15,16,17)(20,22)Polycyclic presentation:
2^4,3^3|a^2=c,b^2=d,b^a=bd,e^a=ef^2,f^a=e^2f^2,e^c=e^2,f^c=f^2g,f^e=fg38 conjugacy classes — view the full character table.
| maximal subgroup of | #11720695, #11720696, #11720709, … |
| maximal normal subgroup of | #11720695, #11720696, #11720709, … |
| maximal quotient of | #11720774, #11720775, #11720776, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 276);