Finite Group DatabasebetaFinite Group Databasebeta| order | 21024 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 74317824 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C23×C32×C4×C73 |
| multiplicative | (ℤ/45656)ˣ, (ℤ/46095)ˣ, (ℤ/49112)ˣ, (ℤ/49168)ˣ, (ℤ/61460)ˣ, (ℤ/63144)ˣ, (ℤ/63216)ˣ, (ℤ/68484)ˣ, (ℤ/73668)ˣ, (ℤ/73836)ˣ, (ℤ/79020)ˣ, (ℤ/92190)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C32×C73 |
| socle, prime radical | C24×C32×C73 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1416 conjugacy classes of subgroups.
21024 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.