Finite Group DatabasebetaFinite Group Databasebeta| order | 15625 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C55 · Schur multiplier (H2) = C59 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center | C25 | C54 |
| commutator, Frattini, socle, cosocle | C5 | C55 |
| prime radical | H(5,𝔽5) | C5 |
| LCS | G ▷ C5 ▷ C1 | |
| UCS | C1 ◁ C25 ◁ G | |
| LECS | G ▷ C5 ▷ C1 | |
42489 conjugacy classes of subgroups.
Polycyclic presentation:
5^6|e^5=f^4,d^a=df,c^b=cf3145 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15625, 122);