Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of SL(2,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| direct product | C2×SL(2,𝔽9) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, socle, hypercenter | C22 | A6 |
| commutator, hypocenter | SL(2,𝔽9) | C2 |
| Frattini, cosocle | C2 | C2×A6 |
| LCS | G ▷ SL(2,𝔽9) | |
| UCS | C1 ◁ C22 | |
73 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
26 conjugacy classes — view the full character table.
| maximal subgroup of | #72209937, C4×SL(2,𝔽9), C22×SL(2,𝔽9), … |
| maximal normal subgroup of | C4×SL(2,𝔽9), C22×SL(2,𝔽9) |
| maximal quotient of | C4×SL(2,𝔽9), C22×SL(2,𝔽9), D5×SL(2,𝔽9), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4598);