Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D3×#107 |
| Fitting | C2×C3×#107 ⋊ C2 |
| Sylow | C3 ⋊ C22×#107 |
600 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 269 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)(10,11,15,17,13,16,12,14);(6,7,8,9)(11,14)(12,15)(16,17);(1,2)(4,5);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1380, #10710068, D3×#1387, … |
| maximal normal subgroup of | D3×#1380, #10710068, D3×#1387, … |
| maximal quotient of | C2×D3×#335, D3×#1567, C2×#68569, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11719);