Finite Group DatabasebetaFinite Group Databasebeta| order | 18864 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1198080 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C32×C4×C131 |
| multiplicative | (ℤ/23933)ˣ, (ℤ/27545)ˣ, (ℤ/30693)ˣ, (ℤ/30771)ˣ, (ℤ/35415)ˣ, (ℤ/40924)ˣ, (ℤ/47866)ˣ, (ℤ/55090)ˣ, (ℤ/61386)ˣ, (ℤ/61542)ˣ, (ℤ/70830)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C32×C131 |
| socle, prime radical | C23×C32×C131 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
324 conjugacy classes of subgroups.
18864 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.