Finite Group DatabasebetaFinite Group Databasebeta| order | 28704 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 11354112 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C3×C4×C13×C23 |
| multiplicative | (ℤ/52311)ˣ, (ℤ/55695)ˣ, (ℤ/58936)ˣ, (ℤ/59032)ˣ, (ℤ/59408)ˣ, (ℤ/62296)ˣ, (ℤ/62895)ˣ, (ℤ/63544)ˣ, (ℤ/67088)ˣ, (ℤ/69748)ˣ, (ℤ/74260)ˣ, (ℤ/83860)ˣ, (ℤ/86256)ˣ, (ℤ/88404)ˣ, (ℤ/88548)ˣ, (ℤ/89676)ˣ, (ℤ/93444)ˣ, (ℤ/95316)ˣ, (ℤ/104622)ˣ, (ℤ/107820)ˣ, (ℤ/111390)ˣ, (ℤ/125790)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C3×C13×C23 |
| socle, prime radical | C24×C3×C13×C23 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
944 conjugacy classes of subgroups.
28704 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.