Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D3×#460 |
| Fitting | C3×#460 ⋊ C2 |
| Sylow | C3 ⋊ C2×#460 |
584 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 15 points:
(5,6,8,10)(7,12,11,9)(13,14,15);(1,2,3,4);(2,4)(6,9)(7,11)(10,12);(14,15)57 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1622, D3×#1620, D3×#1627, … |
| maximal normal subgroup of | D3×#1622, D3×#1620, D3×#1627, … |
| maximal quotient of | D3×#1666, D3×#1668, D3×#1670, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12957);