Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C53 ⋊ #7453 |
102 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 2 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)(55,62,67,64)(56,69)(57,71)(58,60)(59,78)(63,66,82,77)(65,83,76,80)(68,81,84,85)(70,79)(72,75)(73,74);(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)(54,55,57,64,59,77,56,68,58,76,69,80,70,85,71,63,61,67,75,62,79,66,73,84,60,65,74,83,78,81,72,82)Polycyclic presentation:
2^8,53|a^2=d,b^2=eg,c^2=fgh,d^2=efg,e^2=h,f^2=gh,g^2=h,b^a=bc,c^a=ce,e^a=eh,f^a=fh,i^a=i^52,c^b=cf,d^b=def,e^b=eh,f^b=fg,g^b=gh1025 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57228);