Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C53 ⋊ #7452 |
102 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 102 conjugacy classes of subgroups — too many to draw. Only its 51 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) = 13568 |
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)(54,55,57,59)(56,61,60,58)(62,64,67,76)(63,70,72,68)(65,80,66,85)(69,88,87,78)(71,84,79,86)(73,81,77,82)(74,89,83,75)(90,91,93,92);(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)(55,58)(56,60)(59,61)(62,63,66,71,81,78,90,91,69,73,86,85,70,76,83,89,67,72,65,79,82,88,93,92,87,77,84,80,68,64,74,75)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=fg,d^2=efgh,f^2=gh,g^2=h,b^a=bc,c^a=ce,i^a=i^52,c^b=cf,d^b=def,f^b=fg,g^b=gh1037 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57225);