Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #11389 |
836 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 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)(55,61,62,76)(56,64)(58,69)(59,68)(60,72,74,75)(63,67,70,83)(65,79)(66,78)(71,84)(73,77,81,82)(80,85);(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)(54,56)(55,60,62,74)(57,64)(58,66)(59,65)(61,75,76,72)(63,73,70,81)(67,82,83,77)(68,79)(69,78)(71,80)(84,85);(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)(56,60,65,74)(57,67)(58,70)(59,62)(61,69)(63,71)(64,77,79,82)(66,81,80,73)(68,83)(72,85,75,78)(76,84)Polycyclic presentation:
2^8,53|a^2=g,b^2=f,c^2=f,e^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,f^a=fh,i^a=i^52,c^b=cf,d^b=dh,g^b=gh,i^b=i^52,d^c=dh,i^c=i^521190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 78515);