Finite Group DatabasebetaFinite Group Databasebeta| order | 10625 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C53×C17 · Schur multiplier (H2) = C52 |
| direct product | C5×C17×5−1+2 |
| unambiguous semidirect product | C25⋊(C52×C17) |
| unambiguous semidirect product | (C17×C25)⋊C52 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C52×C17 | C52 |
| commutator, Frattini, cosocle | C5 | C53×C17 |
| prime radical | C53×C17 | C5 |
| LCS | G ▷ C5 ▷ C1 | |
| UCS | C1 ◁ C52×C17 ◁ G | |
160 conjugacy classes of subgroups.
2465 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10625, 13);