Finite Group DatabasebetaFinite Group Databasebeta| order | 20736 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 342456532992 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C29×C4×C9 |
| abelian | C23×C4×C8×C92 |
| multiplicative | (ℤ/55480)ˣ, (ℤ/64824)ˣ, (ℤ/66576)ˣ, (ℤ/67488)ˣ, (ℤ/78840)ˣ, (ℤ/82080)ˣ, (ℤ/83220)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C32×C4 | C25×C32 |
| socle, prime radical | C25×C32 | C2×C32×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
53337 conjugacy classes of subgroups.
20736 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.