Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×D16×C53 ⋊ C2 |
| Sylow | C53 ⋊ #13313 |
556 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 99 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:
(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)(55,57)(58,60)(59,66)(61,73)(62,78)(63,72)(64,74)(65,79)(67,83)(68,85)(69,71)(70,84)(75,86)(76,88)(77,87)(80,82)(81,89);(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)(59,65)(60,72)(61,75)(62,63)(66,82)(67,69)(68,80)(70,81)(71,79)(73,87)(74,78)(76,77)(83,84)(85,89);(54,55)(56,57)(58,59)(60,71)(61,65)(62,69)(63,68)(64,70)(66,72)(67,75)(73,82)(74,85)(76,80)(77,81)(78,84)(79,86)(83,87)(88,89)Polycyclic presentation:
2^8,53|d^2=gh,e^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,f^a=fh,g^a=gh,c^b=cf,d^b=dg,e^b=eh,f^b=fh,g^b=gh,e^c=eh,f^c=fh,i^c=i^521184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 88317);