Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #34179 |
2390 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 3392 |
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)(67,75)(72,76)(73,74)(80,81);(66,70,71,69)(67,74,75,73)(68,77,78,79)(72,80,76,81);(59,63)(62,65)(66,69,71,70)(67,73,75,74)(68,77,78,79)(72,80,76,81);(58,60,61,64)(59,62,63,65)(66,68)(67,72)(69,77)(70,79)(71,78)(73,80)(74,81)(75,76);(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)(54,55,56,57)(58,59)(60,62)(61,63)(64,65)(66,67)(68,76)(69,73)(70,74)(71,75)(72,78)(77,81)(79,80)Polycyclic presentation:
2^8,53|a^2=h,b^2=g,c^2=f,d^2=f,b^a=bf,c^a=cg,e^a=ef,i^a=i^52,d^b=df2168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 329637);