Finite Group DatabasebetaFinite Group Databasebeta| order | 18360 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1161216 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C23×C3×C5×C9×C17 |
| multiplicative | (ℤ/21527)ˣ, (ℤ/23639)ˣ, (ℤ/28551)ˣ, (ℤ/30393)ˣ, (ℤ/30591)ˣ, (ℤ/32151)ˣ, (ℤ/38068)ˣ, (ℤ/42868)ˣ, (ℤ/43054)ˣ, (ℤ/47278)ˣ, (ℤ/55116)ˣ, (ℤ/57102)ˣ, (ℤ/60786)ˣ, (ℤ/61182)ˣ, (ℤ/64302)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C23×C32×C5×C17 |
| socle, prime radical | C23×C32×C5×C17 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
640 conjugacy classes of subgroups.
18360 conjugacy classes. The character table is too large to display.
| automorphism group of | C11×C19×C103, C11×C27×C103 |
| outer automorphism group of | C11×C19×C103, C11×C27×C103 |
Past the SmallGroups library coverage — no SmallGroups id.