Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #7303 |
204 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 2 generators on 93 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)(55,58)(57,59)(60,61)(62,64,67,78,66,82,81,93,69,79,80,92,68,77,65,76)(63,70,73,86,84,85,71,75,74,88,89,90,72,87,83,91);(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)(54,55,57,60,58,56,61,59)(62,63,66,72,69,74,68,84)(64,75,77,90,79,91,82,86)(65,73,67,83,81,89,80,71)(70,78,85,76,88,92,87,93)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=f,d^2=gh,e^2=fgh,f^2=h,b^a=bc,c^a=cf,e^a=efg,f^a=fh,i^a=i^52,c^b=cg,d^b=dh1502 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56837);