Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #25751 |
1474 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 89 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)(54,56,57,55)(59,67)(61,75)(65,69)(68,77)(70,88)(74,89)(76,79)(81,82);(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)(58,61,63,76,62,75,64,79)(59,66,68,73,67,84,77,85)(60,70,72,89,71,88,78,74)(65,80,81,83,69,86,82,87);(54,55,57,56)(58,60,62,71)(59,65,67,69)(61,74,75,89)(63,72,64,78)(66,83,84,87)(68,81,77,82)(70,79,88,76)(73,86,85,80);(55,56)(58,59)(60,69)(61,73)(62,67)(63,77)(64,68)(65,71)(66,76)(70,87)(72,81)(74,80)(75,85)(78,82)(79,84)(83,88)(86,89)Polycyclic presentation:
2^8,53|b^2=e,c^2=f,d^2=eh,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,c^b=cg,g^b=gh,d^c=dh,g^c=gh,i^c=i^521184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 224632);