Finite Group DatabasebetaFinite Group Databasebeta| order | 20128 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 73728 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C4 |
| abelian | C4×C8×C17×C37 |
| multiplicative | (ℤ/20413)ˣ, (ℤ/40826)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4 | C22×C17×C37 |
| socle, prime radical | C22×C17×C37 | C2×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
88 conjugacy classes of subgroups.
20128 conjugacy classes. The character table is too large to display.
| automorphism group of | C137×C149 |
| outer automorphism group of | C137×C149 |
Past the SmallGroups library coverage — no SmallGroups id.