Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #9921 |
672 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 81 points:
(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)(55,57)(58,60,62,61)(59,63,64,65)(66,69)(67,72)(68,74)(70,76)(71,77)(73,80)(75,81)(78,79);(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)(58,59,62,64)(60,63,61,65)(66,68,70,75)(67,71,73,78)(69,74,76,81)(72,79,80,77);(54,55)(56,57)(59,63)(60,61)(64,65)(66,67)(68,71)(69,72)(70,73)(74,77)(75,78)(76,80)(79,81)Polycyclic presentation:
2^8,53|b^2=gh,c^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,f^a=fh,c^b=cf,d^b=dg,d^c=dh,i^c=i^521028 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 69810);