Finite Group DatabasebetaFinite Group Databasebeta| order | 336 |
| isoclinism | isoclinic class of #66632 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C3×C7×Q8 ⋊ C2 |
| Hall | C3×C7 ⋊ SD16 |
| Sylow | C7 ⋊ #215 |
| Sylow | C3 ⋊ #1143 |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 168 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,2,4,6,7,5,3)(8,9,10)(11,12,14,16)(13,18,17,15);(2,3)(4,5)(6,7)(9,10)(12,15)(13,17)(16,18)Polycyclic presentation:
2^4,3,7|b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^2,f^a=f^6,c^b=cd57 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#215, #10621064, D3×#1143, … |
| maximal normal subgroup of | D7×#215, #10621064, D3×#1143, … |
| maximal quotient of | #10620647, #10620648, #10620674, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(336, 103);