Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | D3×#417 |
| Fitting | C3×#417 ⋊ C2 |
| Sylow | C3 ⋊ C2×#417 |
816 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)(9,12)(13,14,15);(5,6)(7,12)(8,10)(9,11);(1,2,3,4)(6,9)(7,11)(10,12);(14,15)66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1792, D3×#1793, #10794499, … |
| maximal normal subgroup of | D3×#1792, D3×#1793, #10794499, … |
| maximal quotient of | D3×#1477, D3×#1489, #10761644, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11456);