Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #88545 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | Q8×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ SD16 |
110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 3 generators on 17 points:
(2,5,6)(4,8,9)(10,11,13,15)(12,17,16,14);(2,4)(5,9)(6,8)(11,14)(12,16)(15,17);(1,2,4)(3,6,8)(5,9,7)Polycyclic presentation:
2^4,3^3|b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^2,f^a=f^2,c^b=cd,f^e=fg41 conjugacy classes — view the full character table.
| maximal subgroup of | #11721232, #11721233, #11721234, … |
| maximal normal subgroup of | #11721232, #11721233, #11721234, … |
| maximal quotient of | #11720530, #11720531, #11720583, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 196);