Finite Group DatabasebetaFinite Group Databasebeta| order | 336 |
| isoclinism | isoclinic class of Dic42 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C7 ⋊ C4⋊C4 |
| Sylow | C7 ⋊ Dic3⋊C4 |
| Sylow | C3 ⋊ Dic7⋊C4 |
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)(11,12,13,14)(16,18);(2,3)(4,5)(6,7)(9,10)(15,16,17,18)Polycyclic presentation:
2^4,3,7|a^2=d,b^2=c,b^a=bd,e^a=e^2,f^a=f^690 conjugacy classes — view the full character table.
| maximal subgroup of | #10620885, #10620886, #10620889, … |
| maximal normal subgroup of | #10620885, #10620886, #10620889, … |
| maximal quotient of | #10620646, #10620647, #10620653, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(336, 98);