Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D3×#366 |
| Fitting | C3×#366 ⋊ C2 |
| Sylow | C3 ⋊ C2×#366 |
168 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 168 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) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 23 points:
(5,6,11,17,8,12,15,18,9,13,19,20,14,16,7,10)(21,22,23);(1,2,3,4)(6,10)(7,11)(8,14)(12,20)(13,18)(15,19)(16,17);(22,23)66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1415, D3×#1416, #10715623, … |
| maximal normal subgroup of | D3×#1415, D3×#1416, #10715623, … |
| maximal quotient of | D3×#1371, #10706827, #10706866, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1900);