Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C23×D5×SL(2,𝔽3) |
| unambiguous semidirect product | C5⋊(C24×SL(2,𝔽3)) |
| unambiguous semidirect product | (C2×C5)⋊(C23×SL(2,𝔽3)) |
| Fitting | C23×C5×Q8 ⋊ C2×C3 |
| derived | C5×Q8 ⋊ C24×C3 |
| Hall | C23×Q8×D5 ⋊ C3 |
| Sylow | C5 ⋊ C24×SL(2,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D5×A4 |
| commutator, cosocle, hypocenter | C5×Q8 | C24×C3 |
| Frattini | C2 | C23×D5×A4 |
| Fitting | C23×C5×Q8 | C2×C3 |
| socle | C24×C5 | C2×A4 |
| LCS | G ▷ C5×Q8 | |
| UCS | C1 ◁ C24 | |
3558 conjugacy classes of subgroups; only the 607 normal subgroups are shown.
This group has 3558 conjugacy classes of subgroups — too many to draw. Only its 607 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240349);