Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #6308 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting | C33×C8 ⋊ C2 |
| Sylow | C33 ⋊ M16 |
280 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 216 |
A minimal faithful permutation representation — 4 generators on 17 points:
(1,2,3,6,4,5,7,8)(15,16,17);(2,5)(6,8)(10,11)(13,14)(16,17);(12,13,14);(9,10,11)Polycyclic presentation:
2^4,3^3|b^2=c,c^2=d,b^a=bd,e^a=e^2,f^a=f^2,g^a=g^2114 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3743, C3⋊D3×ΓL(1,𝔽25), #11723323, … |
| maximal normal subgroup of | D3×#3743, C3⋊D3×ΓL(1,𝔽25), #11723323, … |
| maximal quotient of | #11722184, #11722185, #11722190, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 497);