Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C53×#576 ⋊ C2 |
| Sylow | C53 ⋊ #24297 |
1334 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 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)(54,58,60,72,61,73,59,71)(55,63,64,78,65,79,56,67)(57,68,74,84,70,83,69,82)(62,75,76,85,77,81,66,80);(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)(54,57)(55,62)(56,66)(58,68)(59,69)(60,74)(61,70)(63,75)(64,76)(65,77)(67,80)(71,82)(72,84)(73,83)(78,85)(79,81);(54,56,59,65,61,64,60,55)(57,62,69,66,70,77,74,76)(58,67,71,79,73,78,72,63)(68,75,82,80,83,81,84,85);(54,55,61,65)(56,59,64,60)(57,66,70,76)(58,67,73,78)(62,74,77,69)(63,72,79,71)(68,81,83,75)(80,84,85,82)Polycyclic presentation:
2^8,53|a^2=h,b^2=e,d^2=eh,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,f^a=fh,c^b=cg,g^b=gh,f^c=fh,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, 205614);