Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #3672⋊C3 |
| automorphism | Aut(G) = C2×D4×AGL(1,ℤ/9) (order 864) · Inn(G) = #611⋊C3 · Out(G) = C22 |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #3674⋊C3 |
| Sylow | 3−1+2 ⋊ Q16 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,4,7,9,6,3,5,8)(10,12,14,20)(11,15,17,24)(13,22,23,19)(16,25,21,18);(2,4)(3,7)(5,6)(8,9)(10,11,14,17)(12,18,20,25)(13,21,23,16)(15,22,24,19)Polycyclic presentation:
2^2,3,2^2,3^2|a^2=e,b^2=e,d^2=e,f^3=g^2,b^a=bd,d^a=de,f^a=f^2g,g^a=g^2,d^b=de,f^c=fg41 conjugacy classes — view the full character table.
| maximal subgroup of | #63477⋊C3, #63478⋊C3, Q16×AGL(1,ℤ/9), … |
| maximal normal subgroup of | #63477⋊C3, #63478⋊C3, Q16×AGL(1,ℤ/9), … |
| maximal quotient of | #63366⋊C3, #63368⋊C3, #63395⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 162);