Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #88851 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Sylow | C33 ⋊ Q16 |
252 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 432 |
A minimal faithful permutation representation — 4 generators on 25 points:
(1,3,10,14,5,12,4,11)(2,6,13,16,8,15,7,9)(23,24,25);(1,2,5,8)(3,9,12,16)(4,13,10,7)(6,14,15,11)(18,19)(21,22)(24,25);(20,21,22);(17,18,19)Polycyclic presentation:
2^4,3^3|a^2=d,b^2=cd,c^2=d,b^a=bc,c^a=cd,e^a=e^2,f^a=f^2,g^a=g^2111 conjugacy classes — view the full character table.
| maximal subgroup of | #11722009, #11722011, #11722014, … |
| maximal normal subgroup of | #11722009, #11722011, #11722014, … |
| maximal quotient of | #11722186, #11722188, C2×#88853, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 500);