Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #10890 |
676 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)(54,57,59,70,60,71,58,73)(55,62,63,77,64,78,72,76)(56,66,69,82,68,83,67,84)(61,74,65,79,75,85,80,81);(54,56)(55,61,64,75)(57,66)(58,67)(59,69)(60,68)(62,74,78,85)(63,65,72,80)(70,82)(71,83)(73,84)(76,81,77,79);(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)(54,55,59,63,60,64,58,72)(56,65,69,75,68,80,67,61)(57,62,70,77,71,78,73,76)(66,81,82,74,83,79,84,85)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=f,d^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,g^a=gh,i^a=i^52,e^b=eh,d^c=dh1826 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 75613);