Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D3×#465 |
| Fitting | C3×#465 ⋊ C2 |
| Sylow | C3 ⋊ C2×#465 |
564 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 15 points:
(2,4)(13,14,15);(5,6,7,9,8,10,11,12);(1,2)(3,4)(6,9)(7,11)(10,12);(14,15)66 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#465, D3×#3050, D3×#3055, … |
| maximal normal subgroup of | C2×D3×#465, D3×#3050, D3×#3055, … |
| maximal quotient of | D3×#1665, D3×#1671, D3×#1677, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13231);