Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | C37×H(3,𝔽3)⋊C9 ⋊ C3 |
| Sylow | C37 ⋊ #10624788 |
264 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 58 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|b^3=d,b^a=bd,c^a=ce,e^a=ef,c^b=cf,g^b=g^10,g^c=g^26669 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 2626);