Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C53 ⋊ #10748 |
1190 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 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)(58,61)(59,65)(60,69)(62,74)(63,73)(64,76)(66,80)(67,79)(68,82)(70,83)(71,84)(72,85)(75,86)(77,87)(78,88)(81,89);(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)(58,60,62,72,63,70,75,71)(59,64,67,78,66,68,81,77)(61,69,74,85,73,83,86,84)(65,76,79,88,80,82,89,87);(54,55,56,57)(58,59,62,67,63,66,75,81)(60,68,71,78,70,64,72,77)(61,65,74,79,73,80,86,89)(69,76,84,87,83,82,85,88)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^b=eh,f^b=fh,i^b=i^52,d^c=dh1520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 74925);