Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C53×#2352 ⋊ C2 |
| Sylow | C53 ⋊ #34369 |
2410 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)(66,70,71,69)(67,75,73,74)(68,78,77,79)(72,80,76,81);(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)(59,63)(62,64)(66,69,71,70)(67,74,73,75)(68,78,77,79)(72,80,76,81);(58,60,61,65)(59,62,63,64)(67,73)(68,77)(74,75)(78,79);(60,65)(62,64)(66,68)(67,72)(69,79)(70,78)(71,77)(73,76)(74,81)(75,80);(54,55,56,57)(58,59)(60,64)(61,63)(62,65)(66,67)(68,76)(69,75)(70,74)(71,73)(72,77)(78,80)(79,81)Polycyclic presentation:
2^8,53|a^2=h,c^2=fg,d^2=f,e^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,c^b=cg,d^b=df,i^d=i^521376 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 332424);