Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C53×#421 ⋊ C2 |
| Sylow | C53 ⋊ #11032 |
1252 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 generators on 85 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)(54,57)(55,62)(56,67)(58,72)(59,73)(60,74)(61,76)(63,80)(64,70)(65,81)(66,79)(68,83)(69,84)(71,75)(77,85)(78,82);(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)(54,56)(55,61)(57,71)(58,75)(59,68)(60,69)(62,79)(63,78)(64,77)(65,66)(67,73)(70,82)(72,84)(74,83)(76,80)(81,85);(54,55,59,63,60,64,58,65)(56,66,68,61,69,78,75,77)(57,70,72,80,74,62,73,81)(67,82,71,76,84,79,83,85)Polycyclic presentation:
2^8,53|a^2=g,d^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,c^b=cf,d^b=dh,f^b=fh,f^c=fh,g^c=gh,i^c=i^521190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 76422);