Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #9000 |
474 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 3 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)(58,59)(60,65)(61,63)(62,64)(66,69,72,68)(67,73,75,81)(70,79,71,77)(74,76,80,78);(54,56,57,55)(60,64)(62,65)(66,68,72,69)(67,73,75,81)(70,79,71,77)(74,78,80,76);(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)(54,55,57,56)(59,62,63,65)(66,67,70,74,72,75,71,80)(68,76,77,81,69,78,79,73)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,c^2=g,d^2=g,e^2=gh,f^2=g,b^a=bd,c^a=ce,e^a=eg,i^a=i^52,d^b=dg,e^b=eh,f^b=fg,d^c=dh,e^c=egh,f^c=fh1028 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 64490);