Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C2×C4×D3×D4 |
| Fitting | C2×C3×C4×D4 ⋊ C2 |
| Sylow | C3 ⋊ C22×C4×D4 |
2528 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 5 generators on 13 points:
(1,2)(3,4,5)(6,7)(8,9);(1,2)(7,9);(4,5);(10,11,12,13);(1,2)120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18344);