Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C36 |
No aliases for this group.
| Fitting | C37×#6891 ⋊ C3 |
| Sylow | C37 ⋊ H(3,𝔽3)×3−1+2 |
1244 conjugacy classes of subgroups; only the 298 normal subgroups are shown.
This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 298 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=e,b^a=be,c^a=cf,g^a=g^10,d^b=de,g^b=g^26733 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 3578);