Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C53 ⋊ #34215 |
2110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 5 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)(66,69,70,78)(67,73,72,77)(68,76,75,81)(71,79,74,80);(68,75)(71,74)(76,81)(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)(58,60,61,65)(59,62,63,64)(67,72)(71,74)(73,77)(79,80);(54,56,57,55)(66,68,70,75)(67,71,72,74)(69,76,78,81)(73,79,77,80);(54,55,57,56)(58,59,61,63)(60,64,65,62)(66,67)(68,74)(69,77)(70,72)(71,75)(73,78)(76,79)(80,81)Polycyclic presentation:
2^8,53|a^2=h,b^2=gh,c^2=fg,e^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,i^c=i^521856 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 330024);