Finite Group DatabasebetaFinite Group Databasebeta| order | 29088 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 7372800 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4 |
| abelian | C2×C32×C42×C101 |
| multiplicative | (ℤ/39455)ˣ, (ℤ/42455)ˣ, (ℤ/47307)ˣ, (ℤ/54585)ˣ, (ℤ/63076)ˣ, (ℤ/78910)ˣ, (ℤ/84910)ˣ, (ℤ/94614)ˣ, (ℤ/109170)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C23×C32×C101 |
| socle, prime radical | C23×C32×C101 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
648 conjugacy classes of subgroups.
29088 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.