Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #88521 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C3×C9 ⋊ Q16 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 432 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3)(13,15,22,26,17,24,16,23)(14,18,25,28,20,27,19,21);(2,3)(5,7)(6,10)(8,9)(11,12)(13,14,17,20)(15,21,24,28)(16,25,22,19)(18,26,27,23);(4,5,8,10,12,11,6,9,7)Polycyclic presentation:
2^4,3^3|a^2=d,b^2=cd,c^2=d,e^3=g^2,b^a=bc,c^a=cd,e^a=e^2g,f^a=f^2,g^a=g^2111 conjugacy classes — view the full character table.
| maximal subgroup of | #11720233, #11720235, #11720241, … |
| maximal normal subgroup of | #11720233, #11720235, #11720241, … |
| maximal quotient of | #11720539, #11720541, C2×#88521, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 168);