Finite Group DatabasebetaFinite Group Databasebeta| order | 3000 |
| isoclinism | isoclinic class of #1043⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×#1043⋊C5 |
| Fitting | C2×C3×H(3,𝔽5) ⋊ C4 |
| derived | C52 ⋊ C2×C3×C4×C5 |
| Hall | C3×H(3,𝔽5) ⋊ C2×C4 |
| Sylow | H(3,𝔽5) ⋊ C2×C3×C4 |
120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
156 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×(#1043⋊C5)⋊C2 |
| maximal normal subgroup of | C2×C3×(#1043⋊C5)⋊C2 |
Past the SmallGroups library coverage — no SmallGroups id.