Finite Group DatabasebetaFinite Group Databasebeta| order | 26136 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 239500800 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3×C11 |
| abelian | C23×C3×C9×C112 |
| multiplicative | (ℤ/29279)ˣ, (ℤ/32039)ˣ, (ℤ/39999)ˣ, (ℤ/41193)ˣ, (ℤ/41607)ˣ, (ℤ/53332)ˣ, (ℤ/58558)ˣ, (ℤ/64078)ˣ, (ℤ/79998)ˣ, (ℤ/82386)ˣ, (ℤ/83214)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C23×C32×C112 |
| socle, prime radical | C23×C32×C112 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2240 conjugacy classes of subgroups.
26136 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.