Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of C5⋊((C3⋊D3)⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C4×C5⋊((C3⋊D3)⋊C3) |
| unambiguous semidirect product | (C4×C3⋊D15)⋊C3 |
| Fitting | C4×C5×H(3,𝔽3) ⋊ C2 |
| derived | C32×C5 ⋊ C2×C3×C4 |
| Hall | C5×H(3,𝔽3) ⋊ C2×C4 |
| Sylow | H(3,𝔽3) ⋊ C4×D5 |
| Sylow | C5 ⋊ C4×(C3⋊D3)⋊C3 |
124 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 210);