Finite Group DatabasebetaFinite Group Databasebeta| order | 6250 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52×C25 · Schur multiplier (H2) = C52 |
| direct product | C2×C25×5−1+2 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C5×C25 | C52 |
| commutator | C5 | C2×C52×C25 |
| Frattini | C52 | C2×C53 |
| socle | C2×C52 | C53 |
| LCS | G ▷ C5 ▷ C1 | |
| UCS | C1 ◁ C2×C5×C25 ◁ G | |
340 conjugacy classes of subgroups.
1450 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6250, 44);