Finite Group DatabasebetaFinite Group Databasebeta| order | 7025 |
| automorphism | ? |
| homology | Abelianization (H1) = C52 · Schur multiplier (H2) = C5 |
| direct product | C5×C281⋊C5 |
| unambiguous semidirect product | C281⋊C52 |
| unambiguous semidirect product | (C5×C281)⋊C5 |
| Fitting, socle | C5×C281 ⋊ C5 |
| derived, Sylow | C281 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C281⋊C5 |
| commutator, hypocenter | C281 | C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C281 | C5 |
| LCS | G ▷ C281 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
305 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D281⋊C5, C5⋊(D281⋊C5), D5×C281⋊C5, … |
| maximal normal subgroup of | C5×D281⋊C5, C5⋊(D281⋊C5), D5×C281⋊C5, … |
| maximal quotient of | C2×C5×C281⋊C5, C3×C5×C281⋊C5, C25×C281⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7025, 3);