Finite Group DatabasebetaFinite Group Databasebeta| order | 6025 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C241⋊C25 |
| derived, Sylow | C241 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | C241⋊C5 |
| commutator, hypocenter | C241 | C25 |
| Fitting, socle | C5×C241 | C5 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C5 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
5^2,241|a^5=b,c^a=c^91265 conjugacy classes — view the full character table.
| maximal subgroup of | D241⋊C25, C2×C241⋊C25, (C241⋊C3)⋊C25, … |
| maximal normal subgroup of | D241⋊C25, C2×C241⋊C25, (C241⋊C3)⋊C25, … |
| maximal quotient of | C2×C241⋊C25, C3×C241⋊C25, C241⋊C125, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6025, 1);