Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #13372 |
370 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
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)(55,57)(58,60)(59,66)(61,74)(62,77)(63,73)(64,71)(65,80)(67,85)(68,83)(69,84)(70,86)(72,78)(75,89)(76,88)(79,82)(81,87);(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)(56,57)(59,65)(60,71,74,73)(66,83,80,84)(67,81)(68,69)(70,87,88,85)(72,77,82,89)(76,86);(58,59,61,65)(60,70)(62,76,75,86)(63,69,64,68)(66,82)(67,78,81,79)(71,87)(72,80)(73,85)(74,88)(77,84)(83,89)Polycyclic presentation:
2^8,53|a^2=d,b^2=dh,e^2=g,f^2=h,g^2=h,b^a=bd,c^a=ce,e^a=eg,f^a=fh,g^a=gh,c^b=cf,i^b=i^52,d^c=dh,e^c=egh,f^c=fh,g^c=gh872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 88679);