Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C53×#413 ⋊ C2 |
| Sylow | C53 ⋊ #21003 |
1686 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 89 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)(58,62,64,63)(59,67,68,69)(60,71,72,73)(61,75,76,77)(65,79,81,80)(66,82,83,74)(70,85,87,86)(78,84,89,88);(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)(59,66)(60,70)(62,75)(63,77)(64,76)(65,78)(67,82)(68,83)(69,74)(71,85)(72,87)(73,86)(79,84)(80,88)(81,89);(54,56,57,55)(58,60,63,73,64,72,62,71)(59,65,67,79,68,81,69,80)(61,70,77,86,76,87,75,85)(66,78,82,84,83,89,74,88);(54,55,57,56)(58,59,63,69,64,68,62,67)(60,65,71,79,72,81,73,80)(61,74,75,66,76,82,77,83)(70,84,86,78,87,88,85,89)Polycyclic presentation:
2^8,53|a^2=g,b^2=eg,d^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,e^b=eh,f^b=fh,g^b=gh,e^c=eh,f^c=fh,g^c=gh,i^c=i^521208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 171504);