Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C53 ⋊ #20671 |
1324 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)(56,66)(60,74)(64,77)(65,79)(67,81)(73,82)(76,78)(80,85);(54,57)(55,61)(56,65)(58,69)(59,70)(60,73)(62,75)(63,68)(64,76)(66,79)(67,80)(71,83)(72,84)(74,82)(77,78)(81,85);(54,56,58,67,59,66,72,81)(55,60,62,64,63,74,71,77)(57,65,69,80,70,79,84,85)(61,73,75,76,68,82,83,78);(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)(56,64)(57,68,70,61)(58,71)(59,63)(60,67)(62,72)(65,78,79,76)(66,77)(69,75,84,83)(73,80,82,85)(74,81)Polycyclic presentation:
2^8,53|a^2=g,b^2=e,e^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,i^a=i^52,d^b=dh,g^c=gh1826 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 169215);