Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C24 |
| direct product | D5×#5934 |
| Fitting | C5×H(5,𝔽2) ⋊ C2×D3 |
| derived | C5×#997 ⋊ C22 |
| Sylow | C5 ⋊ C2×#5934 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×#1020 |
| commutator, cosocle, hypocenter | C5×#997 | C22 |
| Fitting | C5×H(5,𝔽2) | C2×D3 |
| socle | C2×C5 | C2×#1020 |
| LCS | G ▷ C5×#997 | |
| UCS | C1 ◁ C2 | |
878 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
52 conjugacy classes — view the full character table.
| maximal subgroup of | D5×AGL(3,𝔽2), AGL(1,𝔽5)×#5934, C2×D5×#5934, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#5934, C2×D5×#5934, D5×#73026, … |
| maximal quotient of | C2×D5×#5934, D5×#11715850, D5×#85557, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240256);