Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C3×C37×C27⋊C3 ⋊ C3 |
| Sylow | C37 ⋊ #10624453 |
132 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8991 |
Polycyclic presentation:
3^6,37|a^3=d,d^3=e,b^a=bc,c^a=ce,c^b=cf,g^b=g^261293 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 533);