Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D5×#5429 |
| Fitting | C5×H(5,𝔽2) ⋊ C2×D3 |
| Sylow | C5 ⋊ C2×#5429 |
690 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
68 conjugacy classes — view the full character table.
| maximal subgroup of | D5×SO+(4,𝔽3), AGL(1,𝔽5)×#5429, C2×D5×#5429 |
| maximal normal subgroup of | AGL(1,𝔽5)×#5429, C2×D5×#5429 |
| maximal quotient of | C2×D5×#5429 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239272);