Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #67783 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C3 ⋊ #1356 |
78 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)(4,6,9,18)(5,10,14,27)(7,19,20,24)(8,22,23,17)(11,26,13,15)(12,30,32,33)(16,21,34,28)(25,29,35,31);(2,3)(4,5,7,12,8,13,21,31,9,14,20,32,23,11,28,29)(6,15,16,33,17,10,24,25,18,26,34,30,22,27,19,35)Polycyclic presentation:
2^7,3|a^2=d,b^2=g,c^2=f,d^2=e,e^2=g,b^a=bc,c^a=ce,f^a=fg,h^a=h^2,c^b=cf,d^b=defg,e^b=eg,d^c=dg36 conjugacy classes — view the full character table.
| maximal subgroup of | #10683032, #10683033, #10683035, … |
| maximal normal subgroup of | #10683032, #10683033, #10683035, … |
| maximal quotient of | #10681967, #10682003, #10682354, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 361);