Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | AGL(1,𝔽5)×GU(2,𝔽3) |
| derived | C5×SL(2,𝔽3) ⋊ C42 |
| Sylow | C5 ⋊ C4×GU(2,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | AGL(1,𝔽5)×S4 |
| commutator, hypocenter | C5×SL(2,𝔽3) | C42 |
| Fitting | C5×#41 | C4×D3 |
| socle | C2×C5 | C4×SL(2,ℤ/4) |
| prime radical, cosocle | D5×#41⋊C3 | C22 |
| LCS | G ▷ C5×SL(2,𝔽3) | |
| UCS | C1 ◁ C4 | |
346 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#5429, AGL(1,𝔽5)×GL(2,𝔽5) |
| maximal normal subgroup of | AGL(1,𝔽5)×#5429 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238103);