Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C2×D5×#994 |
| Fitting | C2×C5×H(5,𝔽2) ⋊ C2×C3 |
| Hall | C2×D5×H(5,𝔽2) ⋊ C3 |
| Sylow | C5 ⋊ C22×#994 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D5×A4 |
| commutator, cosocle, hypocenter | C5×Q8 | C24×C3 |
| Frattini | C2 | C23×D5×A4 |
| Fitting | C2×C5×H(5,𝔽2) | C2×C3 |
| socle | C22×C5 | C23×A4 |
| hypercenter | C2×Q8 | D5×A4 |
| LCS | G ▷ C5×Q8 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
2670 conjugacy classes of subgroups; only the 263 normal subgroups are shown.
This group has 2670 conjugacy classes of subgroups — too many to draw. Only its 263 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D5×Ω+(4,𝔽3), C2×D5×#5429, C2×AGL(1,𝔽5)×#994, … |
| maximal normal subgroup of | C2×D5×Ω+(4,𝔽3), C2×D5×#5429, C2×AGL(1,𝔽5)×#994, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240361);