Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of Dic54 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic27⋊C4 |
| Sylow | C27 ⋊ C4⋊C4 |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 432 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,25,24,10,8,5,22,20,23,4,7,26,9,19,14,3,27,6,12,17,13,21,2,18,11,16,15)(28,29,30,31)(33,35);(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)(32,33,34,35)Polycyclic presentation:
2^4,3^3|a^2=d,b^2=c,e^3=f^2g,f^3=g^2,b^a=bd,e^a=e^2f,f^a=f^2g,g^a=g^2114 conjugacy classes — view the full character table.
| maximal subgroup of | C4×Dic54, #11720119, #11720121, … |
| maximal normal subgroup of | C4×Dic54, #11720119, #11720121, … |
| maximal quotient of | #11720047, #11720048, Dic27⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 12);