Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C22 |
| direct product | D5×#5465 |
| unambiguous semidirect product | C5⋊(C2×#5465) |
| Fitting, derived | C5×H(3,𝔽4) ⋊ C2×C3 |
| Hall | D5×H(3,𝔽4) ⋊ C3 |
| Sylow | C5 ⋊ C2×#5465 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D5×C22⋊A4 |
| commutator, Fitting, cosocle, hypocenter | C5×H(3,𝔽4) | C2×C3 |
| socle | C22×C5 | C2×C22⋊A4 |
| LCS | G ▷ C5×H(3,𝔽4) | |
| UCS | C1 ◁ C22 | |
686 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
68 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#11710730, AGL(1,𝔽5)×#5465, D5×#85557, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#5465, D5×#85557, #72258524 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239957);