Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D3×#352 |
| Fitting | C3×#352 ⋊ C2 |
| Sylow | C3 ⋊ C2×#352 |
278 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 57 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) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(4,6,8,14)(5,9,11,17)(7,13,16,19)(10,12,15,18);(4,5)(6,12)(7,15,16,10)(8,11)(9,13,17,19)(14,18);(2,3)39 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#352, D3×#2120, D3×#2121, … |
| maximal normal subgroup of | C2×D3×#352, D3×#2120, D3×#2121, … |
| maximal quotient of | D3×#1317, D3×#1326, #10704439, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1718);