Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1340 |
104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2,3)(4,6,10,17)(5,11,14,27)(7,21,22,33)(8,19,9,18)(12,28,29,35)(13,30,25,26)(15,31,32,20)(16,23,34,24);(2,3)(4,5)(6,15,17,32)(7,20,22,31)(8,13)(9,25)(10,14)(11,16)(12,23,29,24)(18,28,19,35)(21,30)(26,33)(27,34)Polycyclic presentation:
2^7,3|a^2=d,b^2=g,c^2=fg,e^2=g,f^2=g,b^a=bc,c^a=ce,f^a=fg,h^a=h^2,c^b=cf,d^b=defg,e^b=eg,f^b=fg,d^c=dg36 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1340, C2×#67780, #10705336, … |
| maximal normal subgroup of | D3×#1340, C2×#67780, #10705336, … |
| maximal quotient of | #10681866, #10681869, #10681878, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 356);