Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#482 ⋊ C2 |
| Sylow | C3 ⋊ #3094 |
462 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2)(12,14,16,15)(13,17,18,19);(4,6,7,10)(5,9,8,11)(12,13)(14,17)(15,19)(16,18);(2,3)(5,8)(9,11);(4,5)(6,9)(7,8)(10,11)(13,17)(14,15)(18,19)Polycyclic presentation:
2^7,3|c^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^b=h^2,f^c=fg,h^d=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3094, C2×#81373, #11662997, … |
| maximal normal subgroup of | D3×#3094, C2×#81373, #11662997, … |
| maximal quotient of | #10794997, #10795932, #10796433, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13949);