Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#2134 ⋊ C2 |
| Sylow | C53 ⋊ #33373 |
1312 conjugacy classes of subgroups.
| minimal degree | μ(G) = 69 |
| transitive degree | μt(G) = 848 |
A minimal faithful permutation representation — 4 generators on 69 points:
(1,2)(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)(54,56,60,59)(55,63,66,65)(57,68,58,67)(61,64,69,62);(54,57,60,58)(55,62,66,64)(56,67,59,68)(61,63,69,65);(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)(54,56,60,59)(55,61,66,69)(57,67,58,68)(62,63,64,65);(54,55,59,65,60,66,56,63)(57,62,68,61,58,64,67,69)Polycyclic presentation:
2^8,53|a^2=f,b^2=h,c^2=h,d^2=h,e^2=h,f^2=h,b^a=be,e^a=eg,g^a=gh,e^b=eh,f^b=fgh,i^b=i^52,d^c=dh,i^d=i^52,f^e=fh644 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322436);