Finite Group DatabasebetaFinite Group Databasebeta| order | 12050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D241⋊C25 |
| unambiguous semidirect product | (C241⋊C25)⋊C2 |
| derived, Sylow | C241 ⋊ C2×C25 |
| Hall | C241⋊C25 ⋊ C2 |
| Hall | D241 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | D241⋊C5 |
| commutator, hypocenter | C241 | C2×C25 |
| Fitting, socle, cosocle | C5×C241 | C2×C5 |
| prime radical | C5×D241 | C5 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C5 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,241,5|b^5=d,c^a=c^240,c^b=c^91170 conjugacy classes — view the full character table.
| maximal subgroup of | #11757210⋊C25, C2×D241⋊C25, C3×D241⋊C25, … |
| maximal normal subgroup of | #11757210⋊C25, C2×D241⋊C25, C3×D241⋊C25, … |
| maximal quotient of | Dic241⋊C25, C2×D241⋊C25, C3×D241⋊C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12050, 2);