Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×#97 ⋊ C2 |
| Sylow | C3 ⋊ #1955 |
384 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 113 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:
(1,2,3)(8,9,10,11)(12,15,16,17)(13,18,14,19);(5,7)(12,14,17,19,16,13,15,18);(2,3)(4,5,6,7)(9,11)(12,13,17,18,16,14,15,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^2,c^b=cg84 conjugacy classes — view the full character table.
| maximal subgroup of | #10681936, #10686977, #10687326, … |
| maximal normal subgroup of | #10681936, #10686977, #10687326, … |
| maximal quotient of | #10693985, #10693989, #10693994, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2413);