Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×H(7,𝔽2)⋊C5 |
| unambiguous semidirect product | (C3×H(7,𝔽2))⋊C5 |
| Fitting, Hall | C3×H(7,𝔽2) ⋊ C5 |
| Sylow | H(7,𝔽2) ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | C22×C24⋊C5 |
| commutator, cosocle, hypocenter | 2−1+4 | C22×C3×C5 |
| Frattini | C2 | C22×C3×C24⋊C5 |
| Fitting | C3×H(7,𝔽2) | C5 |
| hypercenter | C3×Q8 | C24⋊C5 |
| LCS | G ▷ 2−1+4 | |
| UCS | C1 ◁ C2×C3 ◁ C3×Q8 | |
1238 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 1238 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 240 |
111 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237219);