Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #88431 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ Q16 |
71 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 2 generators on 25 points:
(2,8,6,4,5,9)(3,7)(10,12,14,20)(11,15,17,24)(13,22,23,19)(16,25,21,18);(1,2,4)(3,5,8,7,6,9)(10,11,14,17)(12,18,20,25)(13,21,23,16)(15,22,24,19)Polycyclic presentation:
2^4,3^3|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,f^a=f^2,g^a=g^2,c^b=cd,e^b=e^2,g^b=g^2,f^e=fg29 conjugacy classes — view the full character table.
| maximal subgroup of | #11720691, #11720692, #11720833, … |
| maximal normal subgroup of | #11720691, #11720692, #11720833, … |
| maximal quotient of | #11720313, #11720315, C2×#88433, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 80);