Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C4×D3×M16 |
| Fitting | C3×C4×M16 ⋊ C2 |
| Sylow | C3 ⋊ C2×C4×M16 |
656 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 15 points:
(6,9)(10,12)(13,14,15);(5,6,7,10,8,9,11,12);(14,15);(1,2,3,4)120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1278, #10684681, #10684701, … |
| maximal normal subgroup of | D3×#1278, #10684681, #10684701, … |
| maximal quotient of | D3×C8×M16, D3×#1451, D3×#1453, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11089);