Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #88368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C27 ⋊ SD16 |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 216 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,8,23,9,27,13,11,25,5,4,19,6,21,16,24,22,7,14,12,2,15,10,20,26,3,17,18)(29,32)(30,35)(33,34);(2,5)(3,9)(4,12)(6,7)(8,18)(10,11)(13,20)(14,19)(15,25)(16,24)(17,23)(21,22)(26,27)(28,29,31,34)(30,32,35,33)Polycyclic presentation:
2^4,3^3|a^2=d,c^2=d,e^3=f^2g,f^3=g^2,b^a=bc,c^a=cd,e^a=e^2f,f^a=f^2g,g^a=g^2,c^b=cd72 conjugacy classes — view the full character table.
| maximal subgroup of | #11720160, #11720161, SD16×D27, … |
| maximal normal subgroup of | #11720160, #11720161, SD16×D27, … |
| maximal quotient of | #11720048, #11720049, #11720073, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 15);