Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1860 ⋊ C2 |
| Sylow | C53 ⋊ #26192 |
734 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 93 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)(62,65)(63,71)(64,76)(66,84)(67,82)(68,81)(69,86)(70,72)(73,89)(74,91)(75,77)(78,93)(79,92)(80,83)(85,87)(88,90);(54,57,58,56)(55,59,60,61)(62,65)(63,70)(64,75)(66,81)(67,82)(68,84)(69,85)(71,72)(73,80)(74,91)(76,77)(78,92)(79,93)(83,89)(86,87)(88,90);(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)(54,56,58,57)(55,59,60,61)(62,64,67,78)(63,69,73,87)(65,76,82,93)(66,79,68,77)(70,88,80,91)(71,86,89,85)(72,90,83,74)(75,84,92,81);(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)(56,59)(57,61)(58,60)(62,63)(64,74)(65,80)(66,83)(67,73)(68,72)(69,77)(70,82)(71,81)(75,88)(76,86)(78,90)(79,87)(84,89)(85,93)(91,92)Polycyclic presentation:
2^8,53|b^2=f,c^2=fh,e^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,i^a=i^52,c^b=cg,e^b=eh,g^b=gh,i^b=i^52,g^c=gh,e^d=eh875 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 230059);