Finite Group DatabasebetaFinite Group Databasebeta| order | 7209 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C89 · Schur multiplier (H2) = C32 |
| direct product | C3×3−1+2×C89 |
| unambiguous semidirect product | C9⋊(C32×C89) |
| unambiguous semidirect product | (C9×C89)⋊C32 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C89 | C32 |
| commutator, Frattini | C3 | C33×C89 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C89 ◁ G | |
76 conjugacy classes of subgroups.
2937 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C89×#6857, C89×#6858, C89×#6860, … |
| maximal normal subgroup of | C89×#6857, C89×#6858, C89×#6860, … |
| maximal quotient of | C3×C32⋊C9×C89, C3×C9⋊C9×C89, C9×3−1+2×C89, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7209, 13);