Finite Group DatabasebetaFinite Group Databasebeta| order | 18360 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 120766464 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C33 |
| abelian | C23×C33×C5×C17 |
| multiplicative | (ℤ/22351)ˣ, (ℤ/28737)ˣ, (ℤ/44702)ˣ, (ℤ/57474)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1792 conjugacy classes of subgroups.
18360 conjugacy classes. The character table is too large to display.
| automorphism group of | C7×C31×C103 |
| outer automorphism group of | C7×C31×C103 |
Past the SmallGroups library coverage — no SmallGroups id.