Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | D3×#418 |
| Fitting | C3×#418 ⋊ C2 |
| Sylow | C3 ⋊ C2×#418 |
1008 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 4 generators on 15 points:
(5,7,9,8)(6,11,12,10)(13,14,15);(6,10)(7,8)(11,12);(1,2,3,4)(5,6)(7,11)(8,10)(9,12);(14,15)66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1795, D3×#1883, #10796715, … |
| maximal normal subgroup of | D3×#1795, D3×#1883, #10796715, … |
| maximal quotient of | D3×#1478, D3×#1490, #10761625, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11499);