Finite Group DatabasebetaFinite Group Databasebeta| order | 3125 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C53 · Schur multiplier (H2) = C25 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C52 | C53 |
| prime radical | C53 | C52 |
| LCS | G ▷ C52 ▷ C1 | |
| UCS | C1 ◁ C52 ◁ G | |
| LECS | G ▷ C52 ▷ C1 | |
126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 625 |
Polycyclic presentation:
5^5|b^5=e,c^5=d,b^a=bd,c^a=ce245 conjugacy classes — view the full character table.
| maximal subgroup of | #30626933, #30626935, C5×#15691108, … |
| maximal normal subgroup of | #30626933, #30626935, C5×#15691108, … |
| maximal quotient of | C5×#15691108, #30626966, #30626974, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3125, 51);