Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C35 |
No aliases for this group.
| Fitting | C37×H(5,𝔽3) ⋊ C3 |
| Sylow | C37 ⋊ UT(4,𝔽3) |
560 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 70 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|b^a=bd,c^a=ce,d^a=df,g^a=g^26,e^b=ef,d^c=df1053 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 2344);