Finite Group DatabasebetaFinite Group Databasebeta| order | 4010 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D401⋊C5 |
| unambiguous semidirect product | (C401⋊C5)⋊C2 |
| Fitting, socle, derived, Sylow | C401 ⋊ C2×C5 |
| Hall | C401⋊C5 ⋊ C2 |
| Hall | D401 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C401 | C2×C5 |
| LCS | G ▷ C401 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 401 |
| transitive degree | μt(G) = 401 |
Polycyclic presentation:
2,5,401|c^a=c^400,c^b=c^7250 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D401⋊C5, C3⋊(D401⋊C5), #23756635⋊C2, … |
| maximal normal subgroup of | C3×D401⋊C5, #23756635⋊C2, C5×D401⋊C5, … |
| maximal quotient of | C3×D401⋊C5, C3⋊(D401⋊C5), #23756633⋊C2, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4010, 1);