Finite Group DatabasebetaFinite Group Databasebeta| order | 4525 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C181⋊C25 |
| derived, Sylow | C181 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | C181⋊C5 |
| commutator, hypocenter | C181 | C25 |
| Fitting, socle, prime radical, cosocle | C5×C181 | C5 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C5 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 206 |
| transitive degree | μt(G) = 4525 |
Polycyclic presentation:
5^2,181|a^5=b,c^a=c^59205 conjugacy classes — view the full character table.
| maximal subgroup of | (C181⋊C3)⋊C25, C3×C181⋊C25, C25×C181⋊C5, … |
| maximal normal subgroup of | (C181⋊C3)⋊C25, C3×C181⋊C25, C25×C181⋊C5, … |
| maximal quotient of | C3×C181⋊C25, C181⋊C125, C5×C181⋊C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4525, 1);