Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | D3×#323 |
| Fitting | C3×#323 ⋊ C2 |
| Sylow | C3 ⋊ C2×#323 |
456 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 87 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)(12,14)(13,16)(15,19)(17,18);(4,5,6,8,7,9,10,11)(12,13)(14,18,19,16)(15,17);(2,3)66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1316, D3×#1317, #10704274, … |
| maximal normal subgroup of | D3×#1316, D3×#1317, #10704274, … |
| maximal quotient of | D3×#1270, D3×#1272, #10683136, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 694);