Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C3×#322 ⋊ C2 |
| Sylow | C3 ⋊ #1714 |
198 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 69 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)(5,9)(8,11)(12,13,14,16,15,17,18,19);(4,5,6,8,7,9,10,11);(2,3)(5,8)(6,10)(9,11)(13,16)(14,18)(17,19)Polycyclic presentation:
2^7,3|b^2=d,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^2,c^b=cf66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1714, C2×#68090, #10782916, … |
| maximal normal subgroup of | D3×#1714, C2×#68090, #10782916, … |
| maximal quotient of | #10688972, #10694959, #10694966, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 666);