Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #12569 |
570 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 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)(58,61,64,63)(59,66,68,79)(60,70,74,73)(62,75,78,77)(65,80,82,85)(67,76,83,89)(69,84,81,88)(71,86,72,87);(58,60,62,72,61,70,75,87,64,74,78,71,63,73,77,86)(59,65,67,81,79,85,89,84,68,82,83,69,66,80,76,88);(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)(54,55,56,57)(58,59)(60,69)(61,66)(62,76)(63,79)(64,68)(65,71)(67,77)(70,84)(72,82)(73,88)(74,81)(75,83)(78,89)(80,86)(85,87)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=h,d^2=gh,f^2=gh,g^2=h,b^a=bd,d^a=dg,f^a=fg,g^a=gh,i^a=i^52,d^b=dh2144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84495);