Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1940 |
248 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 3 generators on 19 points:
(2,3)(8,9,10,11)(12,15,16,17)(13,14,18,19);(1,2,3)(5,7)(12,14,17,18,16,19,15,13);(4,5)(6,7)(9,11)(12,13,17,14,16,18,15,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=f,c^2=e,f^2=g,b^a=bd,c^a=ce,c^b=cg,h^c=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1940, C2×#70452, #10798466, … |
| maximal normal subgroup of | D3×#1940, C2×#70452, #10798466, … |
| maximal quotient of | #10693741, #10693746, #10693751, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3028);