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 ⋊ #13285 |
350 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
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)(54,56,57,61)(55,58,59,60)(62,65,67,81,69,82,68,66)(63,71,73,72,74,83,84,86)(64,76,78,93,80,85,79,77)(70,87,88,75,89,91,90,92);(62,64,66,77,68,79,82,85,69,80,81,93,67,78,65,76)(63,70,86,92,84,90,83,91,74,89,72,75,73,88,71,87);(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)(54,55,57,59)(56,60,61,58)(62,63,68,73,69,74,67,84)(64,75,79,91,80,92,78,87)(65,72,66,83,82,86,81,71)(70,85,88,93,89,76,90,77)Polycyclic presentation:
2^8,53|a^2=f,b^2=def,c^2=e,d^2=gh,e^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,g^a=gh,i^a=i^523404 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 88181);