Finite Group DatabasebetaFinite Group Databasebeta| order | 15625 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C53 · Schur multiplier (H2) = C52 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, socle | C52 | C5×H(3,𝔽5) |
| commutator, Frattini, cosocle | C53 | C53 |
| prime radical | C54 | C52 |
| LCS | G ▷ C53 ▷ C52 ▷ C1 | |
| UCS | C1 ◁ C52 ◁ C54 ◁ G | |
| LECS | G ▷ C53 ▷ C52 ▷ C1 | |
270 conjugacy classes of subgroups.
Polycyclic presentation:
5^6|b^5=e^4f^4,c^5=ef^2,b^a=bf,c^a=ce^2,c^b=cd,d^b=de,d^c=df169 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15625, 546);