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 ⋊ #33369 |
1220 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 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)(54,57,60,58)(55,62,64,70)(56,67,66,71)(59,69,74,72)(61,77,76,65)(63,79,81,80)(68,75,73,83)(78,84,85,82);(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)(56,66)(61,76)(65,77)(67,71)(68,73)(75,83)(78,85)(82,84);(54,56)(55,61)(57,67)(58,71)(59,73)(60,66)(62,77)(63,78)(64,76)(65,70)(68,74)(69,83)(72,75)(79,84)(80,82)(81,85);(54,55,59,63,60,64,74,81)(56,65,68,82,66,77,73,84)(57,62,69,79,58,70,72,80)(61,75,78,71,76,83,85,67)Polycyclic presentation:
2^8,53|a^2=f,d^2=h,e^2=h,f^2=h,b^a=be,e^a=eg,g^a=gh,c^b=ch,e^b=eh,f^b=fgh,i^c=i^52,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, 322414);