Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Sylow | C37 ⋊ #10624577 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C33 | C32×C37⋊C3 |
| commutator, socle, prime radical, cosocle | C33×C37 | C33 |
| Fitting | C37×#6855 | C3 |
| hypercenter | #6855 | C37⋊C3 |
| hypocenter | C37 | #10624577 |
| LCS | G ▷ C33×C37 ▷ C37 | |
| UCS | C1 ◁ C33 ◁ #6855 | |
296 conjugacy classes of subgroups.
| transitive degree | μt(G) = 26973 |
Polycyclic presentation:
3^6,37|a^3=def,b^3=de^2,c^3=d,b^a=bd,c^a=ce,g^a=g^10,c^b=cf,g^b=g^10,g^c=g^261293 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 1039);