Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #12715 |
976 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 generators on 85 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)(54,56)(55,61)(57,66)(58,71)(59,68)(60,73)(62,75)(63,78)(64,76)(65,79)(67,72)(69,82)(70,85)(74,81)(77,80)(83,84);(55,60)(57,69)(61,73)(62,64)(63,74)(65,80)(66,82)(70,84)(75,76)(77,79)(78,81)(83,85);(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)(54,55)(56,65,68,78)(57,62,69,60)(58,63)(59,64)(61,67,76,71)(66,81)(70,77,84,74)(72,79)(73,83)(75,85)(80,82)Polycyclic presentation:
2^8,53|a^2=f,d^2=h,e^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^52,d^b=dh,f^b=fgh,e^c=eh,f^c=fh,f^d=fh1178 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85135);