Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #8986 |
532 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 3 generators on 81 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)(58,61,62,63)(59,64,60,65)(66,68)(67,72)(69,76)(70,78)(71,79)(73,81)(74,80)(75,77);(54,56,57,55)(58,60,62,59)(61,65,63,64)(67,71)(70,77)(72,79)(75,78);(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)(54,55,57,56)(58,59,63,64,62,60,61,65)(66,67)(68,74,76,81)(69,71)(70,73)(72,75,79,78)(77,80)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfgh,c^2=g,d^2=g,e^2=h,f^2=g,b^a=bd,c^a=ce,i^a=i^52,d^b=dg,e^b=eh,f^b=fg,d^c=dh,e^c=eh,f^c=fh,i^c=i^521040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 64393);