Finite Group DatabasebetaFinite Group Databasebeta| order | 8125 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C13 · Schur multiplier (H2) = C52 |
| direct product | C13×H(3,𝔽5)⋊C5 |
| unambiguous semidirect product | H(3,𝔽5)⋊(C5×C13) |
| unambiguous semidirect product | (C13×H(3,𝔽5))⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C5×C13 | H(3,𝔽5) |
| commutator, Frattini | C52 | C52×C13 |
| LCS | G ▷ C52 ▷ C5 ▷ C1 | |
| UCS | C1 ◁ C5×C13 ◁ C52×C13 ◁ G | |
64 conjugacy classes of subgroups.
637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8125, 7);