Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#3020 ⋊ C2 |
| Sylow | C53 ⋊ #33568 |
1110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(3,13)(7,24)(12,27)(14,17)(15,20)(23,25)(29,30)(31,32)(33,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35);(2,8)(5,21)(7,23)(9,28)(10,11)(12,29)(15,20)(16,26)(18,22)(24,25)(27,30)(31,32)(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)(2,7)(4,17)(5,20)(6,13)(8,23)(9,27)(10,25)(11,24)(12,16)(14,19)(15,21)(18,31)(22,32)(26,29)(28,30);(1,2)(3,12)(4,16)(5,8)(6,11)(7,14)(9,19)(10,21)(13,27)(15,29)(17,24)(18,26)(20,30)(22,28)(23,31)(25,32)Polycyclic presentation:
2^8,53|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,f^e=fh788 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 323750);