Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C53×#2026 ⋊ C2 |
| Sylow | C53 ⋊ #25904 |
1078 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)(58,61,62,60)(59,65,64,63)(66,69,70,71)(67,74,72,75)(68,77,78,79)(73,81,80,76);(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)(59,64)(63,65)(66,68,69,77,70,78,71,79)(67,73,74,81,72,80,75,76);(54,55)(56,57)(58,60,62,61)(59,63,64,65)(67,72)(73,80)(74,75)(76,81);(58,59,62,64)(60,65,61,63)(66,67,70,72)(68,76,78,81)(69,75,71,74)(73,77,80,79)Polycyclic presentation:
2^8,53|a^2=e,b^2=eh,c^2=ef,d^2=e,f^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,c^b=cg,i^d=i^52890 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 226186);