Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #12631 |
464 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 135 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 — 3 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)(54,56,57,55)(59,65)(64,77)(66,72)(67,79)(68,82)(78,89)(80,81)(83,86);(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)(58,60,62,70,63,71,76,88)(59,64,67,78,65,77,79,89)(61,69,73,84,74,85,75,87)(66,68,80,83,72,82,81,86);(54,55,57,56)(58,59)(60,68)(61,72)(62,67)(63,65)(64,69)(66,74)(70,86)(71,82)(73,81)(75,80)(76,79)(77,85)(78,87)(83,88)(84,89)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=e,d^2=h,f^2=h,b^a=bd,c^a=ch,d^a=dh,f^a=fgh,d^b=dg,g^b=gh,i^b=i^52,f^d=fh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84754);