Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #10045 |
444 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 101 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)(55,59)(57,66)(58,63)(60,69)(61,68)(62,65)(64,67)(70,73,76,89)(71,78,81,96)(72,83,85,99)(74,88,75,90)(77,91,92,101)(79,95,80,97)(82,94,93,98)(84,87,86,100);(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)(59,68)(62,69)(70,72,76,85)(71,77,81,92)(73,87,89,100)(74,86,75,84)(78,94,96,98)(79,93,80,82)(83,90,99,88)(91,97,101,95);(54,55)(56,62)(57,65)(58,61)(59,64)(60,67)(63,69)(66,68)(70,71,76,81)(72,82,85,93)(73,78,89,96)(74,80,75,79)(77,86,92,84)(83,98,99,94)(87,101,100,91)(88,97,90,95)Polycyclic presentation:
2^8,53|a^2=g,b^2=g,c^2=g,d^2=g,e^2=h,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,f^a=fgh,c^b=cf,d^b=dg,e^b=eg,f^b=fg,i^b=i^52,d^c=dh,e^c=eh,f^c=fg707 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 70615);