Finite Group DatabasebetaFinite Group Databasebeta| order | 21504 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 452984832 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C16 |
| abelian | C22×C3×C7×C162 |
| multiplicative | (ℤ/40341)ˣ, (ℤ/45832)ˣ, (ℤ/46784)ˣ, (ℤ/50624)ˣ, (ℤ/53312)ˣ, (ℤ/53788)ˣ, (ℤ/64704)ˣ, (ℤ/65088)ˣ, (ℤ/68748)ˣ, (ℤ/69156)ˣ, (ℤ/80682)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C82 | C24×C3×C7 |
| socle, prime radical | C24×C3×C7 | C82 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
6292 conjugacy classes of subgroups.
21504 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.