Finite Group DatabasebetaFinite Group Databasebeta| order | 6050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#11925897 |
| Fitting, socle, derived | C5×C112 ⋊ C2×C5 |
| Hall | C5×#10597244 ⋊ C2 |
| Sylow | C112 ⋊ C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C112 | C2×C5 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 | |
42 conjugacy classes of subgroups.
Polycyclic presentation:
2,5^2,11^2|c^a=c^4,d^a=d^10,d^b=d^4,e^b=e^983 conjugacy classes — view the full character table.
| maximal subgroup of | #11925898⋊D5, #11925894⋊D5, D5×#11925897, … |
| maximal normal subgroup of | #11925898⋊D5, #11925894⋊D5, D5×#11925897, … |
| maximal quotient of | #27130856, C2×C5⋊#11925897, C3×C5⋊#11925897, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6050, 61);