Finite Group DatabasebetaFinite Group Databasebeta| order | 7209 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AΣL(1,𝔽27) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C89 · Schur multiplier (H2) = C3 |
| direct product | #733×C89 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C89 | H(3,𝔽3) |
| commutator, Frattini | C32 | C32×C89 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C89 ◁ C32×C89 ◁ G | |
26 conjugacy classes of subgroups.
1513 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C89×#6878, C89×#6880, C89×#6881, … |
| maximal normal subgroup of | C89×#6878, C89×#6880, C89×#6881, … |
| maximal quotient of | C89×#6858, C89×#6860, C89×#6861, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7209, 10);