Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #21883 |
954 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 93 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)(54,56,57,60)(55,59,58,61)(63,70)(64,74)(69,76)(71,87)(73,77)(75,82)(86,88)(90,91);(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)(55,58)(59,61)(62,65,66,78)(63,69,70,76)(64,73,74,77)(67,81,80,79)(68,83,72,85)(71,88,87,86)(75,91,82,90)(84,93,89,92);(54,55)(56,59)(57,58)(60,61)(62,64)(63,68)(65,77)(66,74)(67,75)(69,85)(70,72)(71,84)(73,78)(76,83)(79,91)(80,82)(81,90)(86,93)(87,89)(88,92);(55,58)(56,60)(62,63,67,71,66,70,80,87)(64,72,75,89,74,68,82,84)(65,76,79,88,78,69,81,86)(73,83,90,92,77,85,91,93)Polycyclic presentation:
2^8,53|a^2=g,c^2=h,d^2=eh,g^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,c^b=ce,d^b=dh,g^c=gh,i^c=i^521190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 179437);