Finite Group DatabasebetaFinite Group Databasebeta| order | 22356 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 128304 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C22×C3×C23×C81 |
| multiplicative | (ℤ/22657)ˣ, (ℤ/26089)ˣ, (ℤ/33543)ˣ, (ℤ/33777)ˣ, (ℤ/45314)ˣ, (ℤ/52178)ˣ, (ℤ/67086)ˣ, (ℤ/67554)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C27 | C22×C32×C23 |
| socle, prime radical | C22×C32×C23 | C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
180 conjugacy classes of subgroups.
22356 conjugacy classes. The character table is too large to display.
| automorphism group of | C139×C163 |
| outer automorphism group of | C139×C163 |
Past the SmallGroups library coverage — no SmallGroups id.