Finite Group DatabasebetaFinite Group Databasebeta| order | 336 |
| isoclinism | isoclinic class of Dic42 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C7 ⋊ M16 |
| Sylow | C7 ⋊ #208 |
| Sylow | C3 ⋊ #1136 |
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)(12,15)(16,18);(2,3)(4,5)(6,7)(9,10)(11,12,13,16,14,15,17,18)Polycyclic presentation:
2^4,3,7|a^2=c,c^2=d,b^a=bd,e^a=e^2,f^a=f^690 conjugacy classes — view the full character table.
| maximal subgroup of | #10620493, #10620494, #10620496, … |
| maximal normal subgroup of | #10620493, #10620494, #10620496, … |
| maximal quotient of | #10620642, C4⋊(C3⋊(C7⋊C8)), #10620669, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(336, 96);