Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2 |
| direct product | C22×C5×Q8⋊C9 |
| derived | Q8 ⋊ C22×C5×C9 |
| Hall | C22×C5×Q8 ⋊ C9 |
| Sylow | C22×Q8 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical, hypercenter | C23×C3×C5 | A4 |
| commutator, hypocenter | Q8 | C22×C5×C9 |
| Frattini | C2×C3 | C22×C5×A4 |
| Fitting | C22×C3×C5×Q8 | C3 |
| cosocle | C3×Q8 | C22×C3×C5 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C23×C3×C5 | |
202 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1440 |
420 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1625);