Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #11577 |
424 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 91 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) = 3392 |
A minimal faithful permutation representation — 3 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)(59,68)(63,69)(65,66)(70,72,74,79)(71,76,77,83)(73,78,81,85)(75,82,80,84);(54,56)(55,59,62,68)(57,66)(58,64)(60,69,61,63)(65,67)(71,75,77,80)(73,81)(76,82,83,84)(78,85);(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)(54,55,57,61,58,62,67,60)(56,63,66,59,64,69,65,68)(70,71)(72,76)(73,80,81,75)(74,77)(78,84,85,82)(79,83)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=gh,e^2=g,b^a=bd,d^a=df,f^a=fh,i^a=i^52,c^b=cg,d^b=dh,e^b=ef,e^d=eh1025 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 79250);