Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D3×#468 |
| Fitting | C3×#468 ⋊ C2 |
| Sylow | C3 ⋊ C2×#468 |
544 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 15 points:
(2,4)(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)48 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#468, D3×#3054, D3×#3055, … |
| maximal normal subgroup of | C2×D3×#468, D3×#3054, D3×#3055, … |
| maximal quotient of | D3×#1685, D3×#1691, D3×#1697, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13379);