Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1836 ⋊ C2 |
| Sylow | C53 ⋊ #10426 |
444 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 444 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) = 81 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 81 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)(54,56,57,55)(59,62)(60,65)(63,64)(67,72)(69,78)(71,79)(73,74)(75,77)(80,81);(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)(56,57)(58,59)(60,62)(61,63)(64,65)(66,68,70,76)(67,71,74,81)(69,77,78,75)(72,80,73,79);(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)(55,56)(60,65)(62,64)(66,67)(68,71)(69,72)(70,74)(73,78)(75,79)(76,81)(77,80)Polycyclic presentation:
2^8,53|b^2=g,c^2=d,e^2=g,f^2=gh,b^a=bd,c^a=ce,e^a=eg,f^a=fh,i^a=i^52,c^b=cf,e^b=eh,f^b=fgh,i^b=i^52,e^c=eg,f^c=fgh866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 73050);