Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C53×H(3,ℤ/4) ⋊ C2 |
| Sylow | C53 ⋊ #21009 |
1708 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,58,60,59)(55,63,64,73)(56,67,69,68)(57,71,72,74)(61,65,76,80)(62,77,70,78)(66,81,82,83)(75,79,84,85);(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)(54,57)(55,62)(56,66)(58,71)(59,74)(60,72)(61,75)(63,77)(64,70)(65,79)(67,81)(68,83)(69,82)(73,78)(76,84)(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)(54,56,59,68,60,69,58,67)(55,61,63,65,64,76,73,80)(57,66,74,83,72,82,71,81)(62,75,77,79,70,84,78,85);(54,55)(56,65)(57,70,72,62)(58,63)(59,73)(60,64)(61,68)(66,79,82,85)(67,76)(69,80)(71,78,74,77)(75,81,84,83)Polycyclic presentation:
2^8,53|a^2=g,b^2=eg,d^2=h,e^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,f^b=fh,i^b=i^52,e^c=eh,g^c=gh,i^c=i^521202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 171553);