Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1949 |
240 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 240 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:
(1,2,3)(8,9,10,11)(13,17)(16,18);(2,3)(4,6,7,5)(13,16)(14,19)(17,18);(4,5,7,6)(9,11)(12,13)(14,16)(15,17)(18,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=f,c^2=eg,d^2=g,b^a=bd,c^a=ce,d^a=dg,d^b=dg,h^b=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1949, C2×#69540, #10798647, … |
| maximal normal subgroup of | D3×#1949, C2×#69540, #10798647, … |
| maximal quotient of | #10693772, #10693789, #10693826, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2116);