Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#3189 ⋊ C2 |
| Sylow | C53 ⋊ #9955 |
888 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 generators on 77 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)(57,60)(59,61)(62,64,67,74)(63,69,71,77)(65,73,66,75)(68,76,70,72);(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)(58,61)(63,68)(65,66)(69,72)(70,71)(73,75)(76,77);(54,55)(56,58)(57,59)(60,61)(62,63,67,71)(64,72,74,76)(65,68,66,70)(69,75,77,73)Polycyclic presentation:
2^8,53|a^2=g,c^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fgh,c^b=cf,d^b=dg,e^b=eg,i^b=i^52,d^c=dh,e^c=eg869 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 70049);