Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D3×#449 |
| Fitting | C3×#449 ⋊ C2 |
| Sylow | C3 ⋊ C2×#449 |
812 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)(5,7,9,8)(6,10,11,12)(13,14,15);(5,6)(7,10)(8,12)(9,11);(1,2)(3,4)(6,10)(7,8)(11,12);(14,15)57 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#449, D3×#3002, D3×#3005, … |
| maximal normal subgroup of | C2×D3×#449, D3×#3002, D3×#3005, … |
| maximal quotient of | D3×#1597, D3×#1609, D3×#1600, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12657);