Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×D3×M32 |
| Fitting | C2×C3×M32 ⋊ C2 |
| Sylow | C3 ⋊ C22×M32 |
400 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 21 points:
(1,2)(3,4,5)(7,11)(12,17)(13,18)(19,21);(6,7,8,12,9,13,14,19,10,11,15,17,16,18,20,21);(4,5);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1375, #10710035, D3×#1376, … |
| maximal normal subgroup of | D3×#1375, #10710035, D3×#1376, … |
| maximal quotient of | C2×D3×#346, C4×D3×M32, C2×Dic3×M32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14581);