Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2095 ⋊ C2 |
| Sylow | C53 ⋊ #23732 |
1098 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 81 points:
(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)(67,74)(72,75)(73,81)(76,80);(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)(55,57)(66,68,71,79)(67,73,74,81)(69,78,70,77)(72,80,75,76);(54,55)(56,57)(58,60,61,65)(59,62,63,64)(67,72)(69,70)(73,80)(74,75)(76,81)(77,78);(58,59,61,63)(60,64,65,62)(66,67,69,75,71,74,70,72)(68,76,77,73,79,80,78,81)Polycyclic presentation:
2^8,53|a^2=e,b^2=ef,c^2=h,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=dh,c^b=cg,e^b=eh,f^b=fh,e^c=eh,f^c=fh,i^d=i^52884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 199380);