Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#2341 ⋊ C2 |
| Sylow | C53 ⋊ #17606 |
1270 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)(62,65,67,66)(63,68,70,74)(64,71,72,73)(69,76,77,75);(62,64,67,72)(63,69,70,77)(65,73,66,71)(68,75,74,76);(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)(54,56)(55,58)(57,61)(59,60)(62,63)(64,69)(65,68)(66,74)(67,70)(71,76)(72,77)(73,75);(54,55)(56,60,61,58)(57,59)(63,68,70,74)(69,75,77,76)Polycyclic presentation:
2^8,53|a^2=f,c^2=h,d^2=h,e^2=h,b^a=be,e^a=eg,e^b=eh,f^b=fgh,i^b=i^52,d^c=dh1352 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 137198);