Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #68629 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×C22⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ #2034 |
368 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 89 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) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2)(5,7)(8,10,11,9)(13,17)(15,19)(16,18);(4,5)(6,7)(8,9)(10,11)(13,16)(17,18);(2,3)(9,10)(12,13)(14,16)(15,17)(18,19)Polycyclic presentation:
2^7,3|c^2=dg,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^2,c^b=cf,e^c=eg,h^c=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2034, C2×#69935, #10822669, … |
| maximal normal subgroup of | D3×#2034, C2×#69935, #10822669, … |
| maximal quotient of | #10698463, #10698470, #10698553, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2511);