Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #20455 |
1126 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 77 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(63,69)(64,71)(67,70)(72,77);(58,60,61,59)(62,64)(63,68)(65,72)(66,71)(67,74)(69,76)(70,75)(73,77);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55,56,57)(63,67)(65,73)(68,74)(69,70)(72,77)(75,76);(58,59,61,60)(62,63,65,70,66,69,73,67)(64,68,72,75,71,76,77,74)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=efh,e^2=h,f^2=h,b^a=be,d^a=dh,e^b=eh,f^b=fh,i^b=i^52,d^c=dh2168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 167658);