Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C53×#1933 ⋊ C2 |
| Sylow | C53 ⋊ #21094 |
1122 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 77 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)(62,66,68,67)(63,71,73,72)(64,74,75,65)(69,70,77,76);(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)(59,61)(62,65,66,75,68,74,67,64)(63,70,72,77,73,76,71,69);(54,56,57,55)(62,64,67,74,68,75,66,65)(63,69,71,76,73,77,72,70);(54,55,57,56)(58,59)(60,61)(62,63,68,73)(64,70,75,76)(65,69,74,77)(66,71,67,72)Polycyclic presentation:
2^8,53|a^2=g,b^2=eg,c^2=e,d^2=h,e^2=h,f^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,d^b=dh,d^c=dh,i^d=i^521208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 172280);