Finite Group DatabasebetaFinite Group Databasebeta| order | 24000 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 41287680000 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210×C5 |
| abelian | C24×C3×C4×C5×C25 |
| multiplicative | (ℤ/62216)ˣ, (ℤ/66440)ˣ, (ℤ/75144)ˣ, (ℤ/77000)ˣ, (ℤ/79728)ˣ, (ℤ/79992)ˣ, (ℤ/90600)ˣ, (ℤ/93000)ˣ, (ℤ/93324)ˣ, (ℤ/99000)ˣ, (ℤ/99660)ˣ, (ℤ/115500)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C5 | C25×C3×C52 |
| socle, prime radical | C25×C3×C52 | C2×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
19068 conjugacy classes of subgroups.
24000 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.