Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2218 ⋊ C2 |
| Sylow | C53 ⋊ #33837 |
680 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 89 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)(58,61,63,73)(59,67,68,86)(60,69,64,79)(62,76,77,89)(65,80,81,88)(66,83,78,87)(70,85,74,72)(71,82,84,75);(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)(55,57)(58,60,63,64)(59,66,68,78)(61,69,73,79)(62,70,77,74)(65,75,81,82)(67,83,86,87)(71,88,84,80)(72,76,85,89);(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)(58,59,63,68)(60,66,64,78)(61,71,73,84)(62,75,77,82)(65,70,81,74)(67,85,86,72)(69,88,79,80)(76,83,89,87);(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)(56,57)(59,65)(60,64)(61,69)(62,74)(66,82)(67,84)(68,81)(70,77)(71,86)(72,85)(73,79)(75,78)(80,87)(83,88)Polycyclic presentation:
2^8,53|b^2=h,c^2=h,d^2=h,e^2=gh,g^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eg,g^a=gh,i^a=i^52,d^b=de,e^b=eg,g^b=gh,i^b=i^52,i^c=i^52,e^d=eg,g^d=gh,i^d=i^52719 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 326138);