Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C53 ⋊ #7286 |
250 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 75 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) = 6784 |
A minimal faithful permutation representation — 2 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)(54,56,58,66,59,67,57,65)(55,60,62,68,63,69,61,64)(70,71,73,76,74,77,81,85)(72,75,79,82,78,83,80,84);(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)(54,55,57,62,59,63,58,61)(56,64,65,60,67,68,66,69)(71,75)(72,78)(76,84)(77,83)(79,80)(82,85)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=f,d^2=fh,e^2=f,b^a=bc,c^a=cf,e^a=efg,c^b=cg,g^b=gh,i^b=i^52,e^c=eh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56787);