Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C8 |
No aliases for this group.
| Sylow | C53 ⋊ #8156 |
506 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 93 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)(62,65,66,76,67,77,78,89)(63,69,70,82,71,83,84,92)(64,73,75,88,74,87,79,90)(68,80,81,91,72,85,86,93);(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)(54,55,56,58,57,59,60,61)(62,64)(63,68,71,72)(65,73)(66,75)(67,74)(69,80,83,85)(70,81,84,86)(76,88)(77,87)(78,79)(82,91,92,93)(89,90);(62,63,66,70,67,71,78,84)(64,72,75,86,74,68,79,81)(65,69,76,82,77,83,89,92)(73,85,88,93,87,80,90,91)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=e,e^2=g,f^2=h,b^a=bd,f^a=fg,d^b=dg,i^b=i^522168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 60096);