Finite Group DatabasebetaFinite Group Databasebeta| order | 15125 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C4×C5×C11×C25 (order 11000) · Inn(G) = C1 · Out(G) = C2×C4×C5×C11×C25 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C15125 |
| abelian | C121×C125 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C11×C25 | C5×C11 |
| socle, prime radical | C5×C11 | C11×C25 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
12 conjugacy classes of subgroups.
15125 conjugacy classes. The character table is too large to display.
| derived subgroup of | D15125, Dic15125, C2×D15125 |
| Fitting subgroup of | D15125 |
| maximal subgroup of | C2×C121×C125, D15125 |
| maximal normal subgroup of | C2×C121×C125, D15125 |
| maximal quotient of | C2×C121×C125 |
Past the SmallGroups library coverage — no SmallGroups id.