Finite Group DatabasebetaFinite Group Databasebeta| order | 30912 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 2724986880 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210 |
| abelian | C24×C3×C4×C7×C23 |
| multiplicative | (ℤ/76328)ˣ, (ℤ/80840)ˣ, (ℤ/92120)ˣ, (ℤ/96744)ˣ, (ℤ/97008)ˣ, (ℤ/98136)ˣ, (ℤ/110544)ˣ, (ℤ/114492)ˣ, (ℤ/116040)ˣ, (ℤ/121260)ˣ, (ℤ/138180)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C25×C3×C7×C23 |
| socle, prime radical | C25×C3×C7×C23 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
5448 conjugacy classes of subgroups.
30912 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.