Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting | C37×AΣL(1,𝔽27) ⋊ C9 |
| Sylow | C37 ⋊ AΣL(1,𝔽27)⋊C9 |
304 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 69 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=e,c^3=e,b^a=bd,d^a=df,g^a=g^12,c^b=cf,g^c=g^16,g^e=g^26173 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 4354);