Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C22×#135×C53 ⋊ C2 |
| Sylow | C53 ⋊ #23421 |
2094 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 6784 |
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)(62,64,67,74)(63,70,71,77)(65,72,66,73)(68,75,69,76);(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)(59,61)(63,69)(65,66)(68,71)(70,76)(72,73)(75,77);(55,57)(58,59)(60,61)(63,68)(65,66)(69,71)(70,75)(72,73)(76,77);(54,55)(56,57)(62,63)(64,70)(65,68)(66,69)(67,71)(72,75)(73,76)(74,77)Polycyclic presentation:
2^8,53|d^2=h,e^2=h,f^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,c^b=cg,e^b=eh,f^b=fh,e^c=eh,f^c=fh,i^c=i^521520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 196635);