Finite Group DatabasebetaFinite Group Databasebeta| order | 19440 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 53747712 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C33 |
| abelian | C22×C32×C4×C5×C27 |
| multiplicative | (ℤ/23653)ˣ, (ℤ/24661)ˣ, (ℤ/30411)ˣ, (ℤ/31707)ˣ, (ℤ/32643)ˣ, (ℤ/34083)ˣ, (ℤ/34587)ˣ, (ℤ/47306)ˣ, (ℤ/49322)ˣ, (ℤ/60822)ˣ, (ℤ/63414)ˣ, (ℤ/65286)ˣ, (ℤ/68166)ˣ, (ℤ/69174)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C9 | C23×C33×C5 |
| socle, prime radical | C23×C33×C5 | C2×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3888 conjugacy classes of subgroups.
19440 conjugacy classes. The character table is too large to display.
| automorphism group of | C13×C31×C81 |
| outer automorphism group of | C13×C31×C81 |
Past the SmallGroups library coverage — no SmallGroups id.