Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C23 |
| direct product | D5×B(4,𝔽2)⋊C3 |
| unambiguous semidirect product | (D5×B(4,𝔽2))⋊C3 |
| Fitting | C5×B(4,𝔽2) ⋊ C2×C3 |
| derived | C5×H(5,𝔽2) ⋊ C22×C3 |
| Hall | D5×B(4,𝔽2) ⋊ C3 |
| Sylow | C5 ⋊ C2×B(4,𝔽2)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5×#120⋊C3 |
| commutator, cosocle, hypocenter | C5×H(5,𝔽2) | C22×C3 |
| Frattini | C23 | C2×D5×A4 |
| Fitting | C5×B(4,𝔽2) | C2×C3 |
| socle | C2×C5 | C2×#120⋊C3 |
| LCS | G ▷ C5×H(5,𝔽2) | |
| UCS | C1 ◁ C2 | |
486 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | A5×B(4,𝔽2)⋊C3, D5×#11757163, AGL(1,𝔽5)×B(4,𝔽2)⋊C3, … |
| maximal normal subgroup of | AGL(1,𝔽5)×B(4,𝔽2)⋊C3, D5×#73026, #72244483, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237883);