Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C53×#2317 ⋊ C2 |
| Sylow | C53 ⋊ #34184 |
3006 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 5 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)(62,65,66,74)(63,69,68,73)(64,72,71,77)(67,75,70,76);(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)(64,71)(67,70)(72,77)(75,76);(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)(58,59,60,61)(63,68)(67,70)(69,73)(75,76);(62,64)(63,67)(65,72)(66,71)(68,70)(69,75)(73,76)(74,77);(54,55,56,57)(59,61)(62,63)(64,70)(65,73)(66,68)(67,71)(69,74)(72,75)(76,77)Polycyclic presentation:
2^8,53|a^2=h,c^2=fg,e^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,i^c=i^52,i^d=i^521232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 329676);