Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #9082 |
628 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 81 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)(55,57)(66,69,70,76)(67,72,73,79)(68,74,75,80)(71,77,78,81);(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)(58,60,61,65,62,59,63,64)(66,68,70,75)(67,71)(69,74,76,80)(72,77)(73,78)(79,81);(54,55)(56,57)(58,59,61,64,62,60,63,65)(66,67)(68,71,75,78)(69,72)(70,73)(74,77,80,81)(76,79)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfg,c^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,d^b=dg,f^b=fg,i^b=i^521520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 64952);