Finite Group DatabasebetaFinite Group Databasebeta| order | 26448 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 193536 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C3×C4×C19×C29 |
| multiplicative | (ℤ/38605)ˣ, (ℤ/40533)ˣ, (ℤ/43017)ˣ, (ℤ/49605)ˣ, (ℤ/49635)ˣ, (ℤ/52912)ˣ, (ℤ/54044)ˣ, (ℤ/57356)ˣ, (ℤ/66140)ˣ, (ℤ/77210)ˣ, (ℤ/81066)ˣ, (ℤ/86034)ˣ, (ℤ/99210)ˣ, (ℤ/99270)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C3×C19×C29 |
| socle, prime radical | C23×C3×C19×C29 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
216 conjugacy classes of subgroups.
26448 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.