Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #12909 |
314 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 6784 |
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)(54,55,56,57);(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)(58,60,70,86,63,73,77,87,64,74,76,79,62,72,61,71)(59,65,75,84,67,80,82,85,68,81,89,88,78,83,66,69);(55,57)(58,59,62,67,64,68,63,78)(60,69,72,84,74,85,73,88)(61,75,76,82,77,89,70,66)(65,79,80,87,81,86,83,71)Polycyclic presentation:
2^8,53|a^2=f,b^2=dg,c^2=e,d^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^b=i^521220 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86016);