Finite Group DatabasebetaFinite Group Databasebeta| order | 29088 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 103219200 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C23×C32×C4×C101 |
| multiplicative | (ℤ/63128)ˣ, (ℤ/63735)ˣ, (ℤ/67928)ˣ, (ℤ/67984)ˣ, (ℤ/84980)ˣ, (ℤ/87336)ˣ, (ℤ/87408)ˣ, (ℤ/94692)ˣ, (ℤ/101892)ˣ, (ℤ/109260)ˣ, (ℤ/127470)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C32×C101 |
| socle, prime radical | C24×C32×C101 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1416 conjugacy classes of subgroups.
29088 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.