Finite Group DatabasebetaFinite Group Databasebeta| order | 31200 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 61440 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C4 |
| abelian | C3×C4×C8×C13×C25 |
| multiplicative | (ℤ/31613)ˣ, (ℤ/31853)ˣ, (ℤ/39125)ˣ, (ℤ/63226)ˣ, (ℤ/63706)ˣ, (ℤ/78250)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4×C5 | C22×C3×C5×C13 |
| socle, prime radical | C22×C3×C5×C13 | C2×C4×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
264 conjugacy classes of subgroups.
31200 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.