Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C53 ⋊ #7333 |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 2 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)(55,60,62,63,64,74,80,81)(56,65,66,68)(57,69)(61,75,76,85,78,77,79,73)(67,84,83,72)(70,82);(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)(54,55,56,61,57,63,67,77,58,62,68,79,70,74,84,85,59,64,66,78,69,81,83,75,71,80,65,76,82,60,72,73)Polycyclic presentation:
2^8,53|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,g^2=h,b^a=be,d^a=dgh,f^a=fh,i^a=i^52,c^b=cgh,e^b=eh,i^b=i^52,d^c=dh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56905);