Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×C3⋊#6732 |
| unambiguous semidirect product | (C2×C3)⋊#6732 |
| derived | C3×SL(2,𝔽5) ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×A5 |
| commutator, hypocenter | C3×SL(2,𝔽5) | C22 |
| Frattini | C2 | C2×D3×A5 |
| Fitting, socle | C22×C3 | C2×A5 |
| cosocle | C2×C3 | C22×A5 |
| LCS | G ▷ C3×SL(2,𝔽5) | |
| UCS | C1 ◁ C22 | |
218 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 20 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | #72276859, C2×D3×#6732, C2×Ω+(4,𝔽5), … |
| maximal normal subgroup of | C2×D3×#6732, #72277313, C2×#13088295 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4648);