Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C38 |
| unambiguous semidirect product | C37⋊H(3,𝔽9) |
| Fitting | C37×C32⋊H(3,𝔽3) ⋊ C3 |
| Sylow | C37 ⋊ H(3,𝔽9) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C33×C37⋊C3 |
| commutator, socle, cosocle | C32×C37 | C34 |
| Fitting | C37×C32⋊H(3,𝔽3) | C3 |
| hypercenter | C32⋊H(3,𝔽3) | C37⋊C3 |
| hypocenter | C37 | H(3,𝔽9) |
| LCS | G ▷ C32×C37 ▷ C37 | |
| UCS | C1 ◁ C32 ◁ C32⋊H(3,𝔽3) | |
1334 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2997 |
Polycyclic presentation:
3^6,37|b^a=be,c^a=cf,d^a=def,c^b=ce^2f,d^b=de,g^d=g^26701 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 3815);