Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #21828 |
990 conjugacy classes of subgroups; only the 315 normal subgroups are shown.
This group has 990 conjugacy classes of subgroups — too many to draw. Only its 315 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 85 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)(55,61)(59,62)(60,69)(67,68)(70,73,74,81)(71,76,77,83)(72,79,80,85)(75,82,78,84);(54,57,58,66)(55,60,61,69)(56,63,64,65)(59,67,62,68)(70,72)(71,75)(73,79)(74,80)(76,82)(77,78)(81,85)(83,84);(54,56,58,64)(55,59,61,62)(57,65,66,63)(60,68,69,67)(73,81)(76,83)(79,85)(82,84);(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)(56,62)(57,60)(58,61)(59,64)(63,68)(65,67)(66,69)(70,71)(72,78,80,75)(73,76)(74,77)(79,84,85,82)(81,83)Polycyclic presentation:
2^8,53|a^2=g,b^2=e,c^2=e,d^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,i^a=i^52,c^b=ce,d^b=dh,g^c=gh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 179025);