Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #29658 |
1086 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 1086 conjugacy classes of subgroups — too many to draw. Only its 159 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) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 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)(57,65)(60,67)(63,69)(66,68)(70,73,74,80)(71,76,77,83)(72,78,79,84)(75,82,81,85);(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)(54,57)(55,60)(56,63)(58,65)(59,66)(61,67)(62,68)(64,69)(75,81)(82,85);(54,56,58,64)(55,59,61,62)(57,63,65,69)(60,66,67,68)(70,72)(71,75)(73,78)(74,79)(76,82)(77,81)(80,84)(83,85);(54,55,58,61)(56,62,64,59)(57,60,65,67)(63,68,69,66)(70,71)(72,75)(73,76)(74,77)(78,82)(79,81)(80,83)(84,85)Polycyclic presentation:
2^8,53|a^2=e,b^2=e,d^2=h,b^a=be,c^a=cf,g^a=gh,c^b=cg,f^b=fh,d^c=de,i^d=i^52713 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 275466);