Finite Group DatabasebetaFinite Group Databasebeta| order | 26757 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | C32⋊(C991⋊C3) |
| unambiguous semidirect product | C991⋊H(3,𝔽3) |
| unambiguous semidirect product | (C3×C991⋊C3)⋊C3 |
| Fitting | C32×C991 ⋊ C3 |
| Sylow | C991 ⋊ H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×C991⋊C3 |
| commutator, socle, cosocle | C3×C991 | C32 |
| Fitting | C32×C991 | C3 |
| hypercenter | C32 | C991⋊C3 |
| hypocenter | C991 | H(3,𝔽3) |
| LCS | G ▷ C3×C991 ▷ C991 | |
| UCS | C1 ◁ C3 ◁ C32 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8919 |
Polycyclic presentation:
3^3,991|b^a=bc,d^b=d^1132981 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26757, 9);