Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D3×#463 |
| Fitting | C3×#463 ⋊ C2 |
| Sylow | C3 ⋊ C2×#463 |
564 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)(8,12)(9,11)(13,14,15);(1,2,3,4)(6,9)(10,11);(2,4)(5,6)(7,9)(8,10)(11,12);(14,15)57 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#463, D3×#3035, D3×#3036, … |
| maximal normal subgroup of | C2×D3×#463, D3×#3035, D3×#3036, … |
| maximal quotient of | D3×#1677, D3×#1679, D3×#1681, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13108);