Finite Group DatabasebetaFinite Group Databasebeta| order | 21816 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 86400 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C2×C3×C4×C9×C101 |
| multiplicative | (ℤ/22459)ˣ, (ℤ/23047)ˣ, (ℤ/25459)ˣ, (ℤ/32733)ˣ, (ℤ/32751)ˣ, (ℤ/44918)ˣ, (ℤ/46094)ˣ, (ℤ/50918)ˣ, (ℤ/65466)ˣ, (ℤ/65502)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C22×C32×C101 |
| socle, prime radical | C22×C32×C101 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
160 conjugacy classes of subgroups.
21816 conjugacy classes. The character table is too large to display.
| automorphism group of | C37×C607, C19×C1213 |
| outer automorphism group of | C37×C607, C19×C1213 |
Past the SmallGroups library coverage — no SmallGroups id.