Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1411 |
94 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)(7,19,21,32)(8,22,24,17)(11,26,13,15)(12,29,31,34)(16,20,33,23)(25,30,35,28);(2,3)(4,5,7,12,9,14,21,31)(6,15,16,29,18,26,33,34)(8,13,23,30,24,11,20,28)(10,19,25,22,27,32,35,17)Polycyclic presentation:
2^7,3|a^2=d,b^2=g,c^2=fg,d^2=g,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^2,c^b=cfg,d^b=def,e^b=eg,d^c=dfg,e^d=eg39 conjugacy classes — view the full character table.
| maximal subgroup of | #10683021, #10683022, #10683024, … |
| maximal normal subgroup of | #10683021, #10683022, #10683024, … |
| maximal quotient of | #10682572, #10682602, #10682703, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 371);