Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#336 ⋊ C2 |
| Sylow | C3 ⋊ #1924 |
280 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 97 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)(13,14)(18,19);(8,9,11,10)(12,14,16,19,15,13,17,18);(2,3)(4,5)(6,7)(9,10)(12,13,16,18,15,14,17,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^2,c^b=cg,h^c=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1924, C2×#68616, #10797483, … |
| maximal normal subgroup of | D3×#1924, C2×#68616, #10797483, … |
| maximal quotient of | #10693389, #10693396, #10693403, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1192);