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×#421 ⋊ C2 |
| Sylow | C53 ⋊ #21012 |
1732 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)(55,63,65,64)(56,68,69,70)(57,72,74,73)(61,76,77,66)(62,78,71,79)(67,81,83,82)(75,85,84,80);(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)(56,67)(58,72)(59,73)(60,74)(61,75)(63,78)(64,79)(65,71)(66,80)(68,81)(69,83)(70,82)(76,85)(77,84);(54,56)(55,61,65,77)(57,67)(58,68)(59,70)(60,69)(62,75,71,84)(63,76,64,66)(72,81)(73,82)(74,83)(78,85,79,80);(54,55,59,64,60,65,58,63)(56,66,70,77,69,76,68,61)(57,71,72,79,74,62,73,78)(67,80,81,75,83,85,82,84)Polycyclic presentation:
2^8,53|a^2=g,b^2=eg,d^2=h,e^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,f^b=fh,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, 171569);