Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C53×#359 ⋊ C2 |
| Sylow | C53 ⋊ #12990 |
518 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 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)(55,57);(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)(58,60,63,79,64,74,76,73)(59,65,68,87,69,82,84,81)(61,75,62,71,77,72,78,89)(66,83,67,70,85,80,86,88);(54,55)(56,57)(58,59,62,67,63,68,77,85,64,69,78,86,76,84,61,66)(60,70,72,82,73,83,71,87,74,88,75,65,79,80,89,81)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfg,d^2=gh,f^2=g,g^2=h,b^a=bd,c^a=ce,d^b=dg,f^b=fg,g^b=gh,i^c=i^521202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86498);