Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C53×#2021 ⋊ C2 |
| Sylow | C53 ⋊ #25587 |
1332 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 77 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)(54,56,57,61)(55,59,58,60)(63,69)(67,70)(68,76)(75,77);(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)(62,65)(63,68)(64,71,72,73)(66,74)(67,75,70,77)(69,76);(55,58)(59,60)(62,64)(63,67)(65,73)(66,72)(68,75)(69,70)(71,74)(76,77);(54,55)(56,60)(57,58)(59,61)(62,63)(64,70)(65,68)(66,69)(67,72)(71,75)(73,77)(74,76)Polycyclic presentation:
2^8,53|c^2=f,d^2=eh,b^a=be,c^a=cf,d^a=de,g^a=gh,c^b=cg,f^b=fh,g^c=gh,i^d=i^52719 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 222955);