Finite Group DatabasebetaFinite Group Databasebeta| order | 21720 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 241920 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C3×C5×C181 |
| multiplicative | (ℤ/35871)ˣ, (ℤ/38031)ˣ, (ℤ/43448)ˣ, (ℤ/47828)ˣ, (ℤ/50708)ˣ, (ℤ/65172)ˣ, (ℤ/65196)ˣ, (ℤ/71742)ˣ, (ℤ/76062)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
128 conjugacy classes of subgroups.
21720 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.