Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3 |
| direct product | C22×C3×C5×SL(2,𝔽3) |
| Fitting | C22×C3×C5×Q8 ⋊ C3 |
| derived | Q8 ⋊ C22×C32×C5 |
| Hall | C22×C5×Q8 ⋊ C32 |
| Sylow | C22×Q8 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C23×C3×C5 | A4 |
| commutator, cosocle, hypocenter | Q8 | C22×C32×C5 |
| Frattini | C2 | C22×C3×C5×A4 |
| Fitting | C22×C3×C5×Q8 | C3 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C23×C3×C5 | |
328 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
420 conjugacy classes — view the full character table.
| maximal subgroup of | C22×C3×C5×PSU(3,𝔽2)⋊C3, C22×C3×C5×GL(2,𝔽3) |
| maximal normal subgroup of | C22×C3×C5×GL(2,𝔽3) |
| maximal quotient of | C22×C3×C5×PSU(3,𝔽2)⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5754);