Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #33404 |
636 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 636 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)(61,73)(65,77)(66,78)(70,81)(74,83)(79,85)(82,84);(54,56)(55,61)(57,65)(58,66)(59,64)(60,70)(62,73)(63,74)(67,79)(68,77)(69,78)(71,81)(72,82)(75,83)(76,84)(80,85);(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)(54,55,57,60,58,63,67,72,59,62,68,71,69,75,80,76)(56,61,65,70,66,74,79,82,64,73,77,81,78,83,85,84);(55,60,62,71)(57,67)(58,69)(61,70,73,81)(63,76,75,72)(65,79)(66,78)(68,80)(74,84,83,82)(77,85)Polycyclic presentation:
2^8,53|a^2=f,b^2=e,e^2=g,g^2=h,b^a=be,e^a=eg,g^a=gh,f^b=fh,i^b=i^52,d^c=dh1202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322584);