Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C28 |
| direct product | C2×D3×#95 |
| Fitting | C2×C3×#95 ⋊ C2 |
| Sylow | C3 ⋊ C22×#95 |
1880 conjugacy classes of subgroups; only the 661 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 661 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 17 points:
(3,4,5)(6,7,8,9)(10,11)(12,13);(11,13)(14,15,16,17);(1,2)(4,5);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1280, #10684785, D3×#1294, … |
| maximal normal subgroup of | D3×#1280, #10684785, D3×#1294, … |
| maximal quotient of | C4×D3×#95, C2×Dic3×#95, D3×C22⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5938);