Finite Group DatabasebetaFinite Group Databasebeta| order | 10625 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C17 · Schur multiplier (H2) = C52 |
| direct product | C17×H(3,𝔽5)⋊C5 |
| unambiguous semidirect product | H(3,𝔽5)⋊(C5×C17) |
| unambiguous semidirect product | (C17×H(3,𝔽5))⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C5×C17 | H(3,𝔽5) |
| commutator, Frattini, cosocle | C52 | C52×C17 |
| LCS | G ▷ C52 ▷ C5 ▷ C1 | |
| UCS | C1 ◁ C5×C17 ◁ C52×C17 ◁ G | |
64 conjugacy classes of subgroups.
833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10625, 7);