Finite Group DatabasebetaFinite Group Databasebeta| order | 28750 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C4×C11×C125 (order 11000) · Inn(G) = C1 · Out(G) = C2×C4×C11×C125 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C28750 |
| abelian | C2×C23×C625 |
| multiplicative | (ℤ/28751)ˣ, (ℤ/57502)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C125 | C2×C5×C23 |
| socle, prime radical | C2×C5×C23 | C125 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
20 conjugacy classes of subgroups.
28750 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | Dic14375, C2×D14375 |
| maximal subgroup of | Dic14375, C2×D14375 |
| maximal normal subgroup of | Dic14375, C2×D14375 |
| automorphism group of | C28751 |
| outer automorphism group of | C28751 |
Past the SmallGroups library coverage — no SmallGroups id.