Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Sylow | C53 ⋊ #20947 |
1708 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
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)(55,62)(60,75)(61,68)(63,77)(64,78)(74,84)(76,79)(80,85);(54,57)(55,61)(56,65)(58,72)(59,70)(60,74)(62,68)(63,79)(64,80)(66,83)(67,82)(69,73)(71,81)(75,84)(76,77)(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)(54,56,58,71,59,67,73,66)(55,60,63,78,62,75,77,64)(57,65,72,81,70,82,69,83)(61,74,79,85,68,84,76,80);(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)(56,64,67,78)(57,68,70,61)(58,63)(59,62)(60,66,75,71)(65,80)(69,79,72,76)(73,77)(74,81)(82,85)(83,84)Polycyclic presentation:
2^8,53|a^2=g,b^2=eg,e^2=h,b^a=be,c^a=cf,d^a=dh,f^a=fh,i^a=i^52,e^b=eh,f^b=fh,g^b=gh,i^b=i^52,e^c=eh,g^c=gh1202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 171115);