Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D3×#455 |
| Fitting | C3×#455 ⋊ C2 |
| Sylow | C3 ⋊ C2×#455 |
760 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 135 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 — 4 generators on 19 points:
(4,14)(7,12)(9,16)(10,13)(17,18,19);(1,3)(2,6)(4,13)(5,11)(7,16)(8,15)(9,12)(10,14);(1,2,5,8)(3,9,11,16)(4,12,14,7)(6,13,15,10);(18,19)48 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1403, #10715424, D3×#2197, … |
| maximal normal subgroup of | D3×#1403, #10715424, D3×#2197, … |
| maximal quotient of | D3×#1601, D3×#1602, D3×#1607, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12866);