Finite Group DatabasebetaFinite Group Databasebeta| order | 6550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D131⋊C25 |
| unambiguous semidirect product | (C131⋊C25)⋊C2 |
| derived, Sylow | C131 ⋊ C2×C25 |
| Hall | C131⋊C25 ⋊ C2 |
| Hall | D131 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | D131⋊C5 |
| commutator, hypocenter | C131 | C2×C25 |
| Fitting, socle | C5×C131 | C2×C5 |
| LCS | G ▷ C131 | |
| UCS | C1 ◁ C5 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,131,5|b^5=d,c^a=c^130,c^b=c^53115 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D131⋊C25, C3×D131⋊C25, C3⋊(D131⋊C25) |
| maximal normal subgroup of | C2×D131⋊C25, C3×D131⋊C25 |
| maximal quotient of | Dic131⋊C25, C2×D131⋊C25, C3×D131⋊C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6550, 2);