Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×#10587382 |
| Fitting | C2×C5×H(3,𝔽3) ⋊ C4 |
| derived, Hall | C5×H(3,𝔽3) ⋊ C2×C4 |
| Sylow | H(3,𝔽3) ⋊ C2×Dic5 |
| Sylow | C5 ⋊ C2×#1088 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
68 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 325);