Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#2252 ⋊ C2 |
| Sylow | C53 ⋊ #33729 |
474 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 93 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)(63,69)(68,80)(70,82)(71,83)(78,89)(79,92)(81,90)(91,93);(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)(62,64,73,85,66,74,77,86,67,75,87,88,76,84,65,72)(63,68,79,91,71,81,82,89,69,80,92,93,83,90,70,78);(54,56,57,61)(55,58,59,60)(62,63)(64,68)(65,70)(66,71)(67,69)(72,78)(73,79)(74,81)(75,80)(76,83)(77,82)(84,90)(85,91)(86,89)(87,92)(88,93);(54,55,57,59)(56,60,61,58)(64,72)(65,73)(66,76)(68,78)(70,79)(71,83)(74,88)(75,86)(77,87)(80,89)(81,93)(82,92)(84,85)(90,91)Polycyclic presentation:
2^8,53|a^2=e,b^2=e,c^2=fg,f^2=gh,g^2=h,b^a=be,c^a=cf,f^a=fg,g^a=gh,d^b=dh,i^d=i^521040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 325071);