Finite Group DatabasebetaFinite Group Databasebeta| order | 20800 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 35389440 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C42×C13×C25 |
| multiplicative | (ℤ/42824)ˣ, (ℤ/52040)ˣ, (ℤ/53000)ˣ, (ℤ/62448)ˣ, (ℤ/64236)ˣ, (ℤ/78060)ˣ, (ℤ/79500)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C5 | C24×C5×C13 |
| socle, prime radical | C24×C5×C13 | C22×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1494 conjugacy classes of subgroups.
20800 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.