Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | C37×#6855 ⋊ C3 |
| Sylow | C37 ⋊ #10624481 |
144 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2997 |
Polycyclic presentation:
3^6,37|a^3=f,c^3=f^2,b^a=bc,c^a=cd,d^a=df,e^a=ef,g^a=g^10,c^b=ce,d^b=df,e^b=ef,g^b=g^101245 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 625);