Finite Group DatabasebetaFinite Group Databasebeta| order | 7488 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 5945425920 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210×C3 |
| abelian | C24×C32×C4×C13 |
| multiplicative | (ℤ/22120)ˣ, (ℤ/24648)ˣ, (ℤ/26376)ˣ, (ℤ/26544)ˣ, (ℤ/26712)ˣ, (ℤ/28392)ˣ, (ℤ/28440)ˣ, (ℤ/33180)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C25×C32×C13 |
| socle, prime radical | C25×C32×C13 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
8172 conjugacy classes of subgroups.
7488 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.