Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×D3×#99 |
| Fitting | C2×C3×#99 ⋊ C2 |
| Sylow | C3 ⋊ C22×#99 |
1112 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 4 generators on 13 points:
(3,4,5)(6,7)(8,10)(9,11)(12,13);(7,10,11,13)(8,12);(1,2)(4,5);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1390, #10710132, D3×#1393, … |
| maximal normal subgroup of | D3×#1390, #10710132, D3×#1393, … |
| maximal quotient of | C2×D3×#323, C2×D3×#324, D3×#1459, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11263);