Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #12012 |
262 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 85 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)(70,73,75,74)(71,77,78,83)(72,80,82,81)(76,79,84,85);(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)(70,72,74,81,75,82,73,80)(71,76,77,79,78,84,83,85);(54,55,56,59,57,60,62,65,58,61,63,66,64,67,68,69)(70,71)(72,79)(73,77)(74,83)(75,78)(76,81)(80,84)(82,85)Polycyclic presentation:
2^8,53|a^2=e,b^2=d,c^2=f,d^2=f,e^2=g,g^2=h,b^a=bd,d^a=df,i^b=i^522192 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 81166);