Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #11319 |
532 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)(55,61,62,67)(56,64,65,80)(58,69)(59,68)(60,72)(63,77,78,82)(66,81,70,83)(71,75)(73,76)(74,84)(79,85);(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)(55,60,62,73)(57,64,68,80)(58,70)(59,65)(61,76)(63,79,78,74)(66,71)(67,72)(69,83,75,81)(77,84)(82,85);(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)(54,55,58,63,59,62,71,78)(56,60,66,74,65,73,70,79)(57,67,69,82,68,61,75,77)(64,72,81,84,80,76,83,85)Polycyclic presentation:
2^8,53|a^2=g,b^2=de,c^2=d,g^2=h,b^a=bd,c^a=ce,d^a=dh,f^a=fh,i^a=i^52,c^b=cf,d^b=dh,e^b=eh,f^b=fh,g^b=gh,i^b=i^52,e^c=eh,f^c=fh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 78154);