Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Sylow | C37 ⋊ #10624506 |
242 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 31 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 999 |
Polycyclic presentation:
3^6,37|a^3=d,b^3=f,b^a=bc,c^a=ce,e^a=ef,d^b=df^2,g^b=g^26669 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 727);