Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Sylow | C53 ⋊ #20355 |
2018 conjugacy classes of subgroups; only the 987 normal subgroups are shown.
This group has 2018 conjugacy classes of subgroups — too many to draw. Only its 987 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 89 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)(58,62,63,75)(59,66,67,81)(60,70,71,87)(61,72,73,74)(64,77,68,83)(65,78,79,80)(69,84,85,86)(76,88,82,89);(58,61,63,73)(59,65,67,79)(60,69,71,85)(62,74,75,72)(64,76,68,82)(66,80,81,78)(70,86,87,84)(77,89,83,88);(54,55,56,57)(58,60)(59,64)(61,69)(62,70)(63,71)(65,76)(66,77)(67,68)(72,84)(73,85)(74,86)(75,87)(78,88)(79,82)(80,89)(81,83);(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)(58,59)(60,68,71,64)(61,65)(62,66)(63,67)(69,82,85,76)(70,83,87,77)(72,78)(73,79)(74,80)(75,81)(84,89,86,88)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=h,d^2=h,b^a=be,e^a=eh,i^a=i^52,f^b=fh,d^c=dh1850 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 167007);