Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#2204 ⋊ C2 |
| Sylow | C53 ⋊ #33572 |
1108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,5,8,7)(2,11,13,23)(3,16,18,17)(4,19,6,20)(9,25,27,26)(10,21,28,12)(14,24,29,31)(15,30,22,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72)(73,74)(75,76)(77,78)(79,80)(81,82)(83,84);(1,4,8,6)(2,10,13,28)(3,15,18,22)(5,19,7,20)(9,24,27,31)(11,21,23,12)(14,25,29,26)(16,30,17,32)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85);(1,3)(2,9)(4,15)(5,17)(6,22)(7,16)(8,18)(10,24)(11,26)(12,29)(13,27)(14,21)(19,32)(20,30)(23,25)(28,31);(1,2)(3,14)(4,12)(5,11)(6,21)(7,23)(8,13)(9,15)(10,19)(16,24)(17,31)(18,29)(20,28)(22,27)(25,30)(26,32)Polycyclic presentation:
2^8,53|c^2=h,d^2=h,e^2=h,f^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,g^a=gh,d^b=dh,e^b=eh,f^b=fgh,e^c=eg,f^c=fh,i^c=i^52,i^d=i^52,f^e=fh554 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 323781);