Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C53 ⋊ #7095 |
136 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 55 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) = 13568 |
A minimal faithful permutation representation — 2 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)(54,56,59,66)(55,60,64,62)(57,58,68,67)(61,69,63,65)(70,71,74,77)(72,79,81,85)(73,82,80,76)(75,83,84,78);(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)(54,55,57,62,67,63,56,65,59,64,68,60,58,61,66,69)(71,75)(72,78)(73,80)(76,85)(77,84)(79,82)(81,83)Polycyclic presentation:
2^8,53|a^2=d,b^2=g,c^2=fh,d^2=efg,e^2=g,f^2=h,b^a=bc,c^a=ce,e^a=eg,f^a=fg,i^a=i^52,c^b=cf,d^b=defg,e^b=eg,f^b=fh1031 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56296);