Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | D3×#428 |
| Fitting | C3×#428 ⋊ C2 |
| Sylow | C3 ⋊ C2×#428 |
536 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 15 points:
(6,10)(9,12)(13,14,15);(5,6,7,9,8,10,11,12);(1,2,3,4)(6,9)(7,11)(10,12);(14,15)66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1856, D3×#1857, #10796018, … |
| maximal normal subgroup of | D3×#1856, D3×#1857, #10796018, … |
| maximal quotient of | D3×#1565, D3×#1569, #10764212, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11783);