Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C53×#2280 ⋊ C2 |
| Sylow | C53 ⋊ #34174 |
5318 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 3392 |
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)(63,71)(68,72)(69,70)(76,77);(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)(62,66,67,65)(63,70,71,69)(64,73,74,75)(68,76,72,77);(59,61)(62,65,67,66)(63,69,71,70)(64,73,74,75)(68,76,72,77);(62,64,67,74)(63,68,71,72)(65,73,66,75)(69,76,70,77);(54,55,56,57)(58,59)(60,61)(62,63)(64,72)(65,69)(66,70)(67,71)(68,74)(73,77)(75,76)Polycyclic presentation:
2^8,53|a^2=h,b^2=f,c^2=f,d^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,i^d=i^521544 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 329595);