Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #10517 |
344 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 344 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) = 3392 |
A minimal faithful permutation representation — 3 generators on 101 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)(55,61)(56,65)(58,59)(62,63)(66,67)(68,69)(70,73,74,86,75,87,90,101)(71,77,78,94,79,84,88,99)(72,81,82,98,83,85,89,100)(76,91,80,96,92,93,95,97);(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)(55,60)(57,66)(58,67)(59,65)(61,69)(62,64)(63,68)(70,72,75,83)(71,76,79,92)(73,85,87,81)(74,89,90,82)(77,93,84,91)(78,95,88,80)(86,98,101,100)(94,96,99,97);(54,55)(56,64)(57,62)(58,61)(59,63)(60,66)(65,69)(67,68)(70,71,75,79)(72,80,83,95)(73,84,87,77)(74,88,90,78)(76,89,92,82)(81,97,85,96)(86,94,101,99)(91,98,93,100)Polycyclic presentation:
2^8,53|a^2=g,b^2=g,c^2=dh,d^2=g,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,c^b=cf,d^b=dg,f^b=fh,e^c=egh,f^c=fgh,i^c=i^52866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 73664);