Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | D3×Q8⋊C8 |
| Fitting | C3×Q8⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ C2×Q8⋊C8 |
280 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 97 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:
(9,10,12,14)(11,16,15,13)(17,18,19);(1,2,3,5,4,6,7,8)(10,13)(11,15)(14,16);(18,19)84 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×Q8⋊C8, D3×#1476, D3×#1479, … |
| maximal normal subgroup of | C2×D3×Q8⋊C8, D3×#1476, D3×#1479, … |
| maximal quotient of | D3×#1271, D3×#1272, #10683131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 804);