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 ⋊ #10917 |
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)(54,57,58,69,59,68,70,81)(55,61,62,75,63,74,76,84)(56,65,67,80,66,79,71,82)(60,72,73,83,64,77,78,85);(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)(54,56)(55,60,63,64)(57,65)(58,67)(59,66)(61,72,74,77)(62,73,76,78)(68,79)(69,80)(70,71)(75,83,84,85)(81,82);(54,55,58,62,59,63,70,76)(56,64,67,78,66,60,71,73)(57,61,69,75,68,74,81,84)(65,72,80,83,79,77,82,85)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=f,f^2=h,b^a=bd,c^a=ce,g^a=gh,d^b=dh,e^b=eh,i^b=i^52,d^c=dh1202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 75786);