Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C729 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C37 ⋊ C729 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C243 | C37⋊C3 |
| commutator, hypocenter | C37 | C729 |
| Fitting, cosocle | C37×C243 | C3 |
| socle, prime radical | C3×C37 | C243 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C243 | |
14 conjugacy classes of subgroups.
| transitive degree | μt(G) = 26973 |
Polycyclic presentation:
3^6,37|a^3=b,b^3=c,c^3=d,d^3=e,e^3=f,g^a=g^263645 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 505);