Finite Group DatabasebetaFinite Group Databasebeta| order | 9005 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C1801⋊C5 |
| Fitting, socle, derived, Sylow | C1801 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1801 | C5 |
| LCS | G ▷ C1801 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
5,1801|b^a=b^350365 conjugacy classes — view the full character table.
| maximal subgroup of | D1801⋊C5, C2×C1801⋊C5, (C1801⋊C3)⋊C5, … |
| maximal normal subgroup of | D1801⋊C5, C2×C1801⋊C5, (C1801⋊C3)⋊C5, … |
| maximal quotient of | C2×C1801⋊C5, C3×C1801⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9005, 1);