Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | D3×#365 |
| Fitting | C3×#365 ⋊ C2 |
| Sylow | C3 ⋊ C2×#365 |
152 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 67 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:
(1,2,3,6,4,8,9,13,5,7,10,12,11,14,16,15)(17,18,19);(2,6,7,12)(3,9)(4,11)(8,15,14,13)(10,16);(18,19)48 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#365, D3×#2155, #10948201, … |
| maximal normal subgroup of | C2×D3×#365, D3×#2155, #10948201, … |
| maximal quotient of | D3×#1368, #10706743, #10706817, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1887);