Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C53×#368 ⋊ C2 |
| Sylow | C53 ⋊ #12939 |
398 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)(59,67)(60,74)(62,78)(63,77)(64,75)(65,81)(66,69)(68,87)(70,88)(71,89)(72,73)(76,83)(79,85)(80,84)(82,86);(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)(55,57)(58,60,64,77,65,79,83,78)(59,66,70,86,72,87,71,80)(61,74,75,63,81,85,76,62)(67,69,88,82,73,68,89,84);(54,55)(56,57)(58,59,64,70,65,72,83,71)(60,73,77,89,79,67,78,88)(61,80,75,66,81,86,76,87)(62,82,74,68,63,84,85,69)Polycyclic presentation:
2^8,53|a^2=f,b^2=f,d^2=gh,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,g^a=gh,d^b=dg,e^b=eg,g^b=gh,d^c=dg,e^c=eg,g^c=gh,i^c=i^521202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86185);