Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3 |
| Fitting | C3×C4×C5×Q8 ⋊ C3 |
| derived | Q8 ⋊ C32×C4×C5 |
| Hall | C4×C5×Q8 ⋊ C32 |
| Sylow | C4×Q8 ⋊ C32×C5 |
164 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 68 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 | C3×C4×C5×PSU(3,𝔽2)⋊C3, C3×C4×C5×GL(2,𝔽3) |
| maximal normal subgroup of | C3×C4×C5×GL(2,𝔽3) |
| maximal quotient of | C3×C4×C5×PSU(3,𝔽2)⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4104);