Finite Group DatabasebetaFinite Group Databasebeta| order | 31200 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 115192627200 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210×C5 |
| abelian | C25×C3×C52×C13 |
| multiplicative | (ℤ/80696)ˣ, (ℤ/97464)ˣ, (ℤ/103752)ˣ, (ℤ/121044)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
11968 conjugacy classes of subgroups.
31200 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.