Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C24 |
| direct product | C2×D5×#997 |
| unambiguous semidirect product | C5⋊(C22×#997) |
| unambiguous semidirect product | (C2×C5)⋊(C2×#997) |
| Fitting | C2×C5×H(5,𝔽2) ⋊ C2×C3 |
| derived | C5×H(5,𝔽2) ⋊ C22×C3 |
| Hall | C2×D5×H(5,𝔽2) ⋊ C3 |
| Sylow | C5 ⋊ C22×#997 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D5×C22⋊A4 |
| commutator, cosocle, hypocenter | C5×H(5,𝔽2) | C22×C3 |
| Frattini | C2 | C2×D5×C22⋊A4 |
| Fitting | C2×C5×H(5,𝔽2) | C2×C3 |
| socle | C22×C5 | C2×C22⋊A4 |
| LCS | G ▷ C5×H(5,𝔽2) | |
| UCS | C1 ◁ C22 | |
2450 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 2450 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽5)×#997, C2×D5×#5935, C2×#14514395, … |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×#997, C2×D5×#5935, C2×#14514395, … |
| maximal quotient of | D3×D5×#997, D5×#35346⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240382);