Finite Group DatabasebetaFinite Group Databasebeta| order | 7025 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C281⋊C25 |
| derived, Sylow | C281 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | C281⋊C5 |
| commutator, hypocenter | C281 | C25 |
| Fitting, socle | C5×C281 | C5 |
| LCS | G ▷ C281 | |
| UCS | C1 ◁ C5 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
5^2,281|a^5=b,c^a=c^86305 conjugacy classes — view the full character table.
| maximal subgroup of | D281⋊C25, C2×C281⋊C25, C3×C281⋊C25, … |
| maximal normal subgroup of | D281⋊C25, C2×C281⋊C25, C3×C281⋊C25, … |
| maximal quotient of | C2×C281⋊C25, C3×C281⋊C25, C281⋊C125, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7025, 1);