Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Fitting | C53×#2313 ⋊ C2 |
| Sylow | C53 ⋊ #21796 |
1334 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 77 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)(55,59)(58,60)(62,65,66,73)(63,68,69,75)(64,71,72,77)(67,74,70,76);(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)(56,61)(58,60)(62,64)(63,67)(65,71)(66,72)(68,74)(69,70)(73,77)(75,76);(54,56,57,61)(55,58,59,60)(65,73)(68,75)(71,77)(74,76);(54,55)(56,60)(57,59)(58,61)(62,63)(64,70,72,67)(65,68)(66,69)(71,76,77,74)(73,75)Polycyclic presentation:
2^8,53|a^2=g,b^2=e,d^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, 178834);