Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D3×#451 |
| Fitting | C3×#451 ⋊ C2 |
| Sylow | C3 ⋊ C2×#451 |
740 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 155 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 23 points:
(2,4)(21,22,23);(5,7,9,15)(6,10,12,19)(8,17,18,14)(11,20,16,13);(1,2)(3,4)(5,6,9,12)(7,13,15,20)(8,16,18,11)(10,17,19,14);(22,23)57 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1602, D3×#1603, D3×#1605, … |
| maximal normal subgroup of | D3×#1602, D3×#1603, D3×#1605, … |
| maximal quotient of | D3×#1602, D3×#1614, D3×#1605, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12757);