Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#1792 ⋊ C2 |
| Sylow | C53 ⋊ #21473 |
1486 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 73 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)(54,56,57,55)(58,61,63,62)(59,65,66,70)(60,68,69,71)(64,72,73,67);(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)(61,62)(65,70)(67,72)(68,71);(58,60)(59,64)(61,68)(62,71)(63,69)(65,72)(66,73)(67,70);(54,55,57,56)(58,59,63,66)(60,67,69,72)(61,65,62,70)(64,71,73,68)Polycyclic presentation:
2^8,53|a^2=g,d^2=g,e^2=h,b^a=be,c^a=cf,e^a=eh,e^b=eh,f^b=fh,d^c=dh,e^c=eh,i^d=i^52890 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 175481);