Finite Group DatabasebetaFinite Group Databasebeta| order | 6050 |
| automorphism | Aut(G) order 6655000 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3025 |
| unambiguous semidirect product | C25⋊D121 |
| unambiguous semidirect product | C121⋊D25 |
| Fitting, derived, Hall | C25×C121 ⋊ C2 |
| Sylow | C121 ⋊ D25 |
| Sylow | C25 ⋊ D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C25×C121 | C2 |
| Frattini, socle | C5×C11 | D55 |
| LCS | G ▷ C25×C121 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,11,5,11|b^5=d^4,c^11=e^10,b^a=b^4d,c^a=c^10e,d^a=d^4,e^a=e^101514 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D25×D121, C2×D3025, C3×D3025, … |
| maximal normal subgroup of | D25×D121, C2×D3025, C3×D3025 |
| maximal quotient of | Dic3025, C2×D3025, C3×D3025, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6050, 6);