Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #12671 |
310 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 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)(58,61,78,79,65,62,64,63)(59,67,85,68,70,77,69,86)(60,72,75,73,76,74,81,80)(66,82,83,87,84,89,88,71);(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)(54,55,56,57)(58,60)(59,66)(61,72)(62,74)(63,80)(64,81)(65,76)(67,82)(68,87)(69,88)(70,84)(71,86)(73,79)(75,78)(77,89)(83,85);(58,59,63,68,64,69,62,67,65,70,79,86,78,85,61,77)(60,71,74,66,75,82,80,83,76,87,72,84,81,89,73,88)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=deg,d^2=gh,e^2=g,g^2=h,b^a=bd,c^a=ch,d^b=dg,e^b=eg,g^b=gh,i^c=i^521208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84961);