Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | D3×#349 |
| Fitting | C3×#349 ⋊ C2 |
| Sylow | C3 ⋊ C2×#349 |
236 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 77 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:
(1,2,3)(5,9)(6,12)(11,16)(13,18);(4,5,6,10,7,11,13,17,8,9,12,15,14,16,18,19);(2,3)66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1320, #10704307, D3×#1321, … |
| maximal normal subgroup of | D3×#1320, #10704307, D3×#1321, … |
| maximal quotient of | D3×#1314, #10704247, D3×#1322, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1694);