Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C53 ⋊ #33372 |
1176 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)(57,69)(62,76)(67,71)(70,82)(74,84)(77,85)(78,80)(81,83);(54,57)(55,62)(56,67)(58,70)(59,71)(60,69)(61,74)(63,77)(64,78)(65,76)(66,80)(68,81)(72,83)(73,82)(75,84)(79,85);(54,56,60,59)(55,61,65,75)(57,67,69,71)(58,72,73,68)(62,74,76,84)(63,64,79,66)(70,83,82,81)(77,78,85,80);(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)(54,55,59,64,60,65,56,66)(57,62,71,78,69,76,67,80)(58,63,68,75,73,79,72,61)(70,77,81,84,82,85,83,74)Polycyclic presentation:
2^8,53|a^2=f,b^2=h,e^2=h,f^2=h,b^a=be,e^a=eg,g^a=gh,i^a=i^52,e^b=eh,f^b=fgh,d^c=dh,f^e=fh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322433);