Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of D96 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1424 |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 2 generators on 39 points:
(1,2,3)(8,9,15,29,11,16,21,27,23,32,36,31,37,38,10,14,13,18,19,26,24,33,35,34,12,17,30,39,20,25,22,28);(2,3)(4,5,6,7)(9,14)(10,19)(11,20)(12,23)(15,22)(16,31)(17,34)(18,28)(21,30)(24,37)(25,26)(27,32)(29,38)(33,39)(35,36)Polycyclic presentation:
2^7,3|a^2=d,b^2=ceg,c^2=ef,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^2102 conjugacy classes — view the full character table.
| maximal subgroup of | #10683074, #10683075, #10683093, … |
| maximal normal subgroup of | #10683074, #10683075, #10683093, … |
| maximal quotient of | #10682866, #10682888, #10683093, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 168);