Finite Group DatabasebetaFinite Group Databasebeta| order | 29256 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 384384 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C3×C23×C53 |
| multiplicative | (ℤ/35203)ˣ, (ℤ/44619)ˣ, (ℤ/45261)ˣ, (ℤ/59492)ˣ, (ℤ/70406)ˣ, (ℤ/89238)ˣ, (ℤ/90522)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
128 conjugacy classes of subgroups.
29256 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.