Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#2883 ⋊ C2 |
| Sylow | C53 ⋊ #33361 |
1252 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)(57,68)(61,75)(65,79)(69,81)(73,84)(76,82)(78,85)(80,83);(54,57)(55,61)(56,65)(58,69)(59,68)(60,73)(62,76)(63,75)(64,78)(66,80)(67,79)(70,82)(71,83)(72,81)(74,84)(77,85);(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)(54,56,59,67)(55,60,63,74)(57,65,68,79)(58,71,72,66)(61,73,75,84)(62,77,70,64)(69,83,81,80)(76,85,82,78);(54,55)(56,64,67,77)(57,61)(58,70,72,62)(59,63)(60,66)(65,78,79,85)(68,75)(69,82,81,76)(71,74)(73,80)(83,84)Polycyclic presentation:
2^8,53|a^2=f,b^2=h,e^2=h,b^a=be,e^a=eg,g^a=gh,e^b=eh,f^b=fgh,i^b=i^52,d^c=dh,f^e=fh1112 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322380);