Finite Group DatabasebetaFinite Group Databasebeta| order | 23400 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 11520 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C4×C9×C13×C25 |
| multiplicative | (ℤ/24719)ˣ, (ℤ/29255)ˣ, (ℤ/35103)ˣ, (ℤ/35127)ˣ, (ℤ/46804)ˣ, (ℤ/49438)ˣ, (ℤ/58510)ˣ, (ℤ/70206)ˣ, (ℤ/70254)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C5 | C22×C3×C5×C13 |
| socle, prime radical | C22×C3×C5×C13 | C2×C3×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
144 conjugacy classes of subgroups.
23400 conjugacy classes. The character table is too large to display.
| automorphism group of | C19×C1301 |
| outer automorphism group of | C19×C1301 |
Past the SmallGroups library coverage — no SmallGroups id.