Finite Group DatabasebetaFinite Group Databasebeta| order | 336 |
| isoclinism | isoclinic class of #66623 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic84 |
| Hall | C3×C7 ⋊ Q16 |
| Sylow | C7 ⋊ Dic12 |
| Sylow | C3 ⋊ Dic28 |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 336 |
A minimal faithful permutation representation — 2 generators on 26 points:
(1,2,3,4,5,6,7,8)(9,16,15,14,13,12,11,10)(17,18,19)(20,21,22,23,24,25,26);(1,9,5,13)(2,10,6,14)(3,11,7,15)(4,12,8,16)(18,19)(21,26)(22,25)(23,24)Polycyclic presentation:
2^4,3,7|a^2=d,b^2=cd,c^2=d,b^a=bc,c^a=cd,e^a=e^2,f^a=f^687 conjugacy classes — view the full character table.
| maximal subgroup of | #10620477, #10620479, #10620482, … |
| maximal normal subgroup of | #10620477, #10620479, #10620482, … |
| maximal quotient of | #10620655, #10620657, C2×Dic84, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(336, 94);