Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1414 |
84 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)(5,10,13,27)(7,19)(8,23)(9,17)(11,14,28,31)(12,25,22,26)(15,20)(16,24)(18,29,34,30)(21,33)(32,35);(2,3)(4,5)(6,14,16,29)(7,18,20,34)(8,22,24,12)(9,13)(10,15,25,32)(11,21)(17,31,23,30)(19,26,33,27)(28,35)Polycyclic presentation:
2^7,3|a^2=d,b^2=f,c^2=f,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^2,c^b=cfg,d^b=defg,e^b=eg,d^c=dfg,e^d=eg39 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1414, C2×#67782, #10715558, … |
| maximal normal subgroup of | D3×#1414, C2×#67782, #10715558, … |
| maximal quotient of | #10682580, #10682594, #10682724, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 358);