Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | D3×#340 |
| Fitting | C3×#340 ⋊ C2 |
| Sylow | C3 ⋊ C2×#340 |
512 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 193 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) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(5,6,7,8)(9,10,12,15,13,16,11,14)(17,18,19);(1,2,3,4)(10,14)(11,12)(15,16);(18,19)84 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1347, D3×#1348, #10705417, … |
| maximal normal subgroup of | D3×#1347, D3×#1348, #10705417, … |
| maximal quotient of | D3×#1277, #10684651, #10684661, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1441);