Finite Group DatabasebetaFinite Group Databasebeta| order | 3125 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C54 · Schur multiplier (H2) = C55 |
| direct product | C5×#10597837 |
| subgroup | G/H | |
|---|---|---|
| center | C5×C25 | C52 |
| commutator, Frattini, cosocle | C5 | C54 |
| socle | C52 | C53 |
| prime radical | C5×H(3,𝔽5) | C5 |
| LCS | G ▷ C5 ▷ C1 | |
| UCS | C1 ◁ C5×C25 ◁ G | |
| LECS | G ▷ C5 ▷ C1 | |
1186 conjugacy classes of subgroups.
| minimal degree | μ(G) = 130 |
| transitive degree | μt(G) = 625 |
725 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#15691117, C25×#10597837, C52×#10597837, … |
| maximal normal subgroup of | C5×#15691117, C25×#10597837, C52×#10597837, … |
| maximal quotient of | C25×#10597837, C52×#10597837, C5×#15691099, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3125, 74);