Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #7146 |
210 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 91 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)(54,56,58,57,59,65,67,66)(55,60,63,68,61,64,69,62)(70,72,74,82,75,81,73,80)(71,76,77,79,78,84,83,85);(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)(54,55,57,62,58,63,65,60,59,61,66,68,67,69,56,64)(70,71)(72,79,81,85)(73,77)(74,83)(75,78)(76,80,84,82)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=fh,d^2=g,e^2=f,g^2=h,b^a=bc,c^a=ch,e^a=efh,d^b=df,i^b=i^521520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56418);