Finite Group DatabasebetaFinite Group Databasebeta| order | 336 |
| isoclinism | isoclinic class of Dic42 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊Dic21 |
| Hall | C3×C7 ⋊ C4⋊C4 |
| Sylow | C7 ⋊ C4⋊Dic3 |
| Sylow | C3 ⋊ C4⋊Dic7 |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 336 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,2,4,6,7,5,3)(8,9,10)(15,16,17,18);(2,3)(4,5)(6,7)(9,10)(11,12,13,14)(16,18)Polycyclic presentation:
2^4,3,7|a^2=c,b^2=d,b^a=bd,e^a=e^2,f^a=f^690 conjugacy classes — view the full character table.
| maximal subgroup of | #10620500, #10620502, #10620506, … |
| maximal normal subgroup of | #10620500, #10620502, #10620506, … |
| maximal quotient of | C4⋊(C3⋊(C7⋊C8)), #10620656, #10620657, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(336, 99);