Finite Group DatabasebetaFinite Group Databasebeta| order | 18720 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 884736 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C32×C5×C8×C13 |
| multiplicative | (ℤ/22673)ˣ, (ℤ/24101)ˣ, (ℤ/29109)ˣ, (ℤ/29151)ˣ, (ℤ/30987)ˣ, (ℤ/32823)ˣ, (ℤ/38812)ˣ, (ℤ/45346)ˣ, (ℤ/48202)ˣ, (ℤ/58218)ˣ, (ℤ/58302)ˣ, (ℤ/61974)ˣ, (ℤ/65646)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C23×C32×C5×C13 |
| socle, prime radical | C23×C32×C5×C13 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
912 conjugacy classes of subgroups.
18720 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.