Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#3407 ⋊ C2 |
| Sylow | C53 ⋊ #33388 |
1128 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1128 conjugacy classes of subgroups — too many to draw. Only its 351 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 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)(56,64)(61,76)(65,78)(66,79)(73,84)(77,82)(80,83)(81,85);(54,56)(55,61)(57,65)(58,66)(59,64)(60,73)(62,76)(63,77)(67,80)(68,81)(69,78)(70,79)(71,82)(72,83)(74,84)(75,85);(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)(56,61)(57,68)(58,71)(59,62)(60,72)(63,70)(64,76)(65,81)(66,82)(67,74)(69,75)(73,83)(77,79)(78,85)(80,84);(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)(55,60,62,74)(57,67)(58,70)(61,73,76,84)(63,68,71,75)(65,80)(66,79)(69,72)(77,81,82,85)(78,83)Polycyclic presentation:
2^8,53|a^2=f,e^2=g,g^2=h,b^a=be,e^a=eg,g^a=gh,i^a=i^52,e^b=egh,f^b=fh,g^b=gh,i^b=i^52,d^c=dh1826 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322516);