Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #27675 |
740 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 3392 |
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)(62,65,69,68,67,63,66,75)(64,72,71,76,74,70,73,77);(56,60)(58,61)(62,64)(63,70)(65,72)(66,73)(67,74)(68,76)(69,71)(75,77);(54,56)(55,58)(57,60)(59,61)(62,63,69,75,67,65,66,68)(64,70,71,77,74,72,73,76);(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)(54,55,57,59)(56,58,60,61)(63,68)(64,71)(65,75)(66,69)(73,74)(76,77)Polycyclic presentation:
2^8,53|a^2=g,b^2=eh,d^2=eh,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,f^a=fh,i^a=i^52,c^b=cg,f^c=fh1502 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 251552);