Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C43 |
No aliases for this group.
| Fitting | C53×#1726 ⋊ C2 |
| Sylow | C53 ⋊ #33308 |
1618 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1618 conjugacy classes of subgroups — too many to draw. Only its 331 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) = 6784 |
A minimal faithful permutation representation — 4 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)(58,59,60,61)(64,71)(69,76)(72,75)(73,77);(54,55,56,57)(62,64)(63,69)(65,72)(66,71)(67,73)(68,75)(70,76)(74,77);(62,63,68,74,66,70,65,67)(64,69,75,77,71,76,72,73);(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)(55,57)(59,61)(63,67)(65,68)(69,73)(70,74)(72,75)(76,77)Polycyclic presentation:
2^8,53|b^2=eh,c^2=f,d^2=g,e^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eh,i^a=i^52,d^c=dh2132 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322125);