Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | D5×#577⋊C3 |
| unambiguous semidirect product | (D5×#577)⋊C3 |
| Fitting | C5×#577 ⋊ C2×C3 |
| Hall | D5×#577 ⋊ C3 |
| Sylow | C5 ⋊ C2×#577⋊C3 |
690 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | D5×GL(2,𝔽3)⋊A4, D5×#3585⋊C3 |
| maximal normal subgroup of | D5×#3585⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239863);