Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C53 ⋊ #12759 |
1556 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 1556 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 848 |
A minimal faithful permutation representation — 3 generators on 65 points:
(7,12)(13,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15);(6,9)(7,12)(10,11);(1,2,3,4)(5,6)(7,10,12,9)(8,11)(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)(56,57)(58,59)(60,61)(62,63)(64,65)Polycyclic presentation:
2^8,53|a^2=f,d^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^52,d^b=dh,e^b=egh,f^b=fgh,d^c=dg,e^d=eh,f^d=fh1340 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85369);