Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | D3×#469 |
| Fitting | C3×#469 ⋊ C2 |
| Sylow | C3 ⋊ C2×#469 |
596 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 15 points:
(2,4)(6,11)(9,12)(13,14,15);(5,6,10,12,8,11,7,9);(1,2)(3,4)(6,9)(7,10)(11,12);(14,15)48 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1339, D3×#1341, D3×#2190, … |
| maximal normal subgroup of | D3×#1339, D3×#1341, D3×#2190, … |
| maximal quotient of | D3×#1687, D3×#1693, D3×#1701, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13438);