Finite Group DatabasebetaFinite Group Databasebeta| order | 6250 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C53 · Schur multiplier (H2) = C54 |
| direct product | C2×#15691123 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C5 | C5×H(3,𝔽5) |
| commutator, Frattini | C52 | C2×C53 |
| LCS | G ▷ C52 ▷ C5 ▷ C1 | |
| UCS | C1 ◁ C2×C5 ◁ C2×C53 ◁ G | |
396 conjugacy classes of subgroups.
298 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6250, 66);