Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D3×#355 |
| Fitting | C3×#355 ⋊ C2 |
| Sylow | C3 ⋊ C2×#355 |
260 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 57 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) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(2,6)(3,10)(7,9)(8,15)(11,12)(14,16)(17,18,19);(1,2,4,8,5,9,13,16)(3,7,11,15,10,6,12,14);(18,19)39 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1403, #10715424, D3×#1406, … |
| maximal normal subgroup of | D3×#1403, #10715424, D3×#1406, … |
| maximal quotient of | D3×#1318, D3×#1324, #10704458, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1739);