Finite Group DatabasebetaFinite Group Databasebeta| order | 6250 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #15691069⋊C2 |
| Fitting, derived, Sylow | #15691069 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | #15691069 | C2 |
| Frattini | C53 | C5⋊D5 |
| socle | C52 | #6953 |
| LCS | G ▷ #15691069 | |
| UCS | C1 | |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2,5^5|b^5=e^2f,c^5=e^2,b^a=b^4d^3e^3f^2,c^a=c^4d^3e^2f^4,d^a=def^2,e^a=e^4,f^a=f^4,c^b=cd,d^b=de,d^c=df82 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6250, 99);