Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #3746⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | #3745⋊C3 |
| Fitting | C8×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ D8 |
85 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,2,6,8,4,7,3,5)(9,10,16)(11,13,15)(12,14,17);(2,5)(3,6)(7,8)(10,12)(11,14)(13,15)(16,17)Polycyclic presentation:
2^2,3,2^2,3^2|b^2=de,d^2=e,b^a=bd,d^a=de,f^a=f^2,g^a=g^2,f^c=fg53 conjugacy classes — view the full character table.
| maximal subgroup of | #11720248, #11720249, #11720253, … |
| maximal normal subgroup of | #11720248, #11720249, #11720253, … |
| maximal quotient of | #63626⋊C3, #63627⋊C3, #63628⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 118);