Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C23 |
| direct product | C2×C5⋊#5931 |
| unambiguous semidirect product | (C2×C5)⋊#5931 |
| Fitting | C23×C5×Q8 ⋊ D3 |
| derived | C5×C22⋊SL(2,𝔽3) ⋊ C22 |
| Sylow | C5 ⋊ C2×#5931 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C5⋊#1020 |
| commutator, cosocle, hypocenter | C5×C22⋊SL(2,𝔽3) | C22 |
| Frattini | C2 | C2×C5⋊#1020 |
| Fitting | C23×C5×Q8 | D3 |
| socle | C24×C5 | S4 |
| LCS | G ▷ C5×C22⋊SL(2,𝔽3) | |
| UCS | C1 ◁ C22 | |
620 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
78 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240322);