Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2175 ⋊ C2 |
| Sylow | C53 ⋊ C4×#510 |
674 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)(59,65)(64,79)(66,81)(67,77)(68,85)(72,84)(80,83)(82,88);(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)(54,56,57,55);(58,60,63,71)(59,64,65,79)(61,73,76,89)(62,78,74,70)(66,82,81,88)(67,83,77,80)(68,84,85,72)(69,86,87,75);(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)(54,55,57,56)(58,59)(60,68)(61,72)(62,77)(63,65)(64,69)(66,75)(67,74)(70,88)(71,85)(73,83)(76,84)(78,82)(79,87)(80,89)(81,86)Polycyclic presentation:
2^8,53|a^2=f,b^2=h,c^2=f,e^2=gh,g^2=h,b^a=be,d^a=dh,e^a=eg,g^a=gh,i^a=i^52,e^b=eg,g^b=gh,i^c=i^52,i^d=i^52896 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322900);