Finite Group DatabasebetaFinite Group Databasebeta| order | 22176 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 4423680 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4 |
| abelian | C2×C32×C42×C7×C11 |
| multiplicative | (ℤ/25259)ˣ, (ℤ/30095)ˣ, (ℤ/50518)ˣ, (ℤ/60190)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C23×C32×C7×C11 |
| socle, prime radical | C23×C32×C7×C11 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1296 conjugacy classes of subgroups.
22176 conjugacy classes. The character table is too large to display.
| automorphism group of | C13×C29×C67 |
| outer automorphism group of | C13×C29×C67 |
Past the SmallGroups library coverage — no SmallGroups id.