Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D3×SD64 |
| Fitting | C3×SD64 ⋊ C2 |
| Sylow | C3 ⋊ C2×SD64 |
112 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 35 points:
(2,7)(3,12)(4,13)(5,17)(8,9)(10,28)(11,22)(14,31)(15,23)(16,20)(18,26)(19,21)(24,32)(25,27)(29,30)(33,34,35);(1,2,6,11)(3,7,15,22)(4,16,18,32)(5,19,17,10)(8,23,25,12)(9,26,27,13)(14,28,29,21)(20,31,24,30);(34,35)57 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×SD64, D3×#2262, D3×#2263, … |
| maximal normal subgroup of | C2×D3×SD64, D3×#2262, D3×#2263, … |
| maximal quotient of | D3×#1415, D3×#1416, D3×#1424, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1954);