Finite Group DatabasebetaFinite Group Databasebeta| order | 2880 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 49152 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C4×C5×C8×C9 |
| multiplicative | (ℤ/3895)ˣ, (ℤ/4015)ˣ, (ℤ/4551)ˣ, (ℤ/5475)ˣ, (ℤ/5535)ˣ, (ℤ/5792)ˣ, (ℤ/6068)ˣ, (ℤ/7300)ˣ, (ℤ/7790)ˣ, (ℤ/8030)ˣ, (ℤ/9102)ˣ, (ℤ/10950)ˣ, (ℤ/11070)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C4 | C23×C3×C5 |
| socle, prime radical | C23×C3×C5 | C2×C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
486 conjugacy classes of subgroups.
2880 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.