Finite Group DatabasebetaFinite Group Databasebeta| order | 22400 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 491520 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C4×C7×C16×C25 |
| multiplicative | (ℤ/34239)ˣ, (ℤ/34887)ˣ, (ℤ/35751)ˣ, (ℤ/42015)ˣ, (ℤ/42375)ˣ, (ℤ/44816)ˣ, (ℤ/44864)ˣ, (ℤ/45652)ˣ, (ℤ/46516)ˣ, (ℤ/47668)ˣ, (ℤ/56020)ˣ, (ℤ/56500)ˣ, (ℤ/68478)ˣ, (ℤ/69774)ˣ, (ℤ/71502)ˣ, (ℤ/84030)ˣ, (ℤ/84750)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C5×C8 | C23×C5×C7 |
| socle, prime radical | C23×C5×C7 | C2×C5×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
648 conjugacy classes of subgroups.
22400 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.