Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #7231 |
270 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 87 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) = 3392 |
A minimal faithful permutation representation — 2 generators on 93 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)(55,58)(57,61)(59,60)(62,64,67,78,66,77,81,92,68,79,82,93,80,91,65,76)(63,69,72,84,73,85,88,90,74,86,87,89,71,83,70,75);(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)(56,60,61,58)(57,59)(62,63,66,71,68,74,80,73)(64,75,77,89,79,90,91,84)(65,72,67,70,81,87,82,88)(69,78,83,92,86,93,85,76)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=fgh,d^2=h,e^2=fg,f^2=h,b^a=bc,c^a=cf,e^a=efgh,f^a=fh,d^b=dg,i^b=i^521196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56643);