Finite Group DatabasebetaFinite Group Databasebeta| order | 15625 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C53 · Schur multiplier (H2) = C53 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, socle | C5 | C5×H(3,𝔽5)⋊C5 |
| commutator, Frattini, cosocle | C53 | C53 |
| prime radical | C52×H(3,𝔽5) | C5 |
| LCS | G ▷ C53 ▷ C52 ▷ C5 ▷ C1 | |
| UCS | C1 ◁ C5 ◁ C53 ◁ C54 ◁ G | |
| LECS | G ▷ C53 ▷ C52 ▷ C5 ▷ C1 | |
652 conjugacy classes of subgroups.
Polycyclic presentation:
5^6|c^5=f^4,b^a=bf,c^b=cd,d^c=de,e^c=ef265 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15625, 574);