Finite Group DatabasebetaFinite Group Databasebeta| order | 10805 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C2161⋊C5 |
| Fitting, socle, derived, Sylow | C2161 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C2161 | C5 |
| LCS | G ▷ C2161 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
5,2161|b^a=b^953437 conjugacy classes — view the full character table.
| maximal subgroup of | D2161⋊C5, C2×C2161⋊C5, (C2161⋊C3)⋊C5, … |
| maximal normal subgroup of | D2161⋊C5, C2×C2161⋊C5, (C2161⋊C3)⋊C5, … |
| maximal quotient of | C2×C2161⋊C5, C3×C2161⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10805, 1);