Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | D3×#501 |
| Fitting | C3×#501 ⋊ C2 |
| Sylow | C3 ⋊ C2×#501 |
384 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 145 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 — 4 generators on 19 points:
(9,10,11,13,12,14,15,16)(17,18,19);(1,3,4,8)(2,5,6,7)(10,14)(13,16);(1,2,4,6)(3,7,8,5)(10,13)(11,15)(14,16);(18,19)48 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1661, D3×#1660, D3×#1664, … |
| maximal normal subgroup of | D3×#1661, D3×#1660, D3×#1664, … |
| maximal quotient of | D3×#1847, D3×#1943, D3×#1944, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14548);