Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D3×#328 |
| Fitting | C3×#328 ⋊ C2 |
| Sylow | C3 ⋊ C2×#328 |
336 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 77 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:
(1,3,4,8)(2,5,6,7)(9,10)(11,15)(12,14)(13,16)(17,18,19);(1,2)(3,7,8,5)(4,6)(10,13,14,15);(18,19)57 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#328, D3×#1500, D3×#1501, … |
| maximal normal subgroup of | C2×D3×#328, D3×#1500, D3×#1501, … |
| maximal quotient of | D3×#1271, D3×#1272, #10683148, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 908);