Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #17415 |
1008 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 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)(70,73,75,74)(71,77,79,78)(72,80,81,82)(76,83,84,85);(54,57,58,65)(55,60,61,67)(56,63,64,69)(59,66,62,68)(70,72,75,81)(71,76,79,84)(73,82,74,80)(77,85,78,83);(54,56)(55,59)(57,63)(58,64)(60,66)(61,62)(65,69)(67,68);(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)(56,62,64,59)(57,60)(58,61)(63,68,69,66)(65,67)(70,71,74,78,75,79,73,77)(72,76,80,83,81,84,82,85)Polycyclic presentation:
2^8,53|a^2=f,c^2=gh,d^2=h,f^2=h,b^a=be,e^a=eg,i^a=i^52,f^b=fg,d^c=dh1355 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 135785);