Finite Group DatabasebetaFinite Group Databasebeta| order | 30912 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 202752 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C3×C7×C16×C23 |
| multiplicative | (ℤ/34357)ˣ, (ℤ/37177)ˣ, (ℤ/39151)ˣ, (ℤ/47121)ˣ, (ℤ/47517)ˣ, (ℤ/47799)ˣ, (ℤ/49317)ˣ, (ℤ/61888)ˣ, (ℤ/62828)ˣ, (ℤ/63356)ˣ, (ℤ/65756)ˣ, (ℤ/68714)ˣ, (ℤ/74354)ˣ, (ℤ/78302)ˣ, (ℤ/94242)ˣ, (ℤ/95034)ˣ, (ℤ/95598)ˣ, (ℤ/98634)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8 | C23×C3×C7×C23 |
| socle, prime radical | C23×C3×C7×C23 | C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
392 conjugacy classes of subgroups.
30912 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.