Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #88545 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ Q16 |
99 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 3 generators on 25 points:
(2,5,6)(4,8,9)(10,12,14,20)(11,15,17,24)(13,22,23,19)(16,25,21,18);(2,4)(5,9)(6,8)(10,11,14,17)(12,18,20,25)(13,21,23,16)(15,22,24,19);(1,2,4)(3,6,8)(5,9,7)Polycyclic presentation:
2^4,3^3|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^2,f^a=f^2,c^b=cd,f^e=fg41 conjugacy classes — view the full character table.
| maximal subgroup of | #11721236, #11721237, #11721238, … |
| maximal normal subgroup of | #11721236, #11721237, #11721238, … |
| maximal quotient of | #11720529, #11720532, #11720583, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 197);