Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C53×#2360 ⋊ C2 |
| Sylow | C53 ⋊ #34203 |
3038 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 5 generators on 77 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)(62,66,67,65)(63,69,70,75)(64,72,73,74)(68,77,71,76);(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)(63,69,70,75)(64,72,73,74)(68,76,71,77);(59,61);(54,56,57,55)(62,64)(63,68)(65,74)(66,72)(67,73)(69,77)(70,71)(75,76);(54,55,57,56)(58,59)(60,61)(62,63)(64,71)(65,69)(66,75)(67,70)(68,73)(72,77)(74,76)Polycyclic presentation:
2^8,53|a^2=h,b^2=h,d^2=f,e^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,i^e=i^521388 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 329885);