Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2355 ⋊ C2 |
| Sylow | C53 ⋊ #22526 |
1066 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 81 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)(58,60,61,65)(59,63,62,64)(68,76)(71,75)(77,81)(79,80);(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)(67,72)(68,76)(70,78)(71,79)(73,74)(75,80);(58,59,61,62)(60,64,65,63)(66,68,69,76)(67,71,73,75)(70,77,78,81)(72,80,74,79);(54,55,56,57)(59,62)(63,64)(66,67)(68,75)(69,73)(70,72)(71,76)(74,78)(77,79)(80,81)Polycyclic presentation:
2^8,53|a^2=g,b^2=e,d^2=eh,f^2=h,b^a=be,c^a=cf,f^a=fh,c^b=ch,d^b=de,f^c=fh,i^c=i^521358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 186233);