Finite Group DatabasebetaFinite Group Databasebeta| order | 31200 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 10321920 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C3×C4×C13×C25 |
| multiplicative | (ℤ/63832)ˣ, (ℤ/64024)ˣ, (ℤ/72856)ˣ, (ℤ/78040)ˣ, (ℤ/79000)ˣ, (ℤ/93648)ˣ, (ℤ/93672)ˣ, (ℤ/95748)ˣ, (ℤ/96036)ˣ, (ℤ/109284)ˣ, (ℤ/117060)ˣ, (ℤ/118500)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C5 | C24×C3×C5×C13 |
| socle, prime radical | C24×C3×C5×C13 | C2×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1416 conjugacy classes of subgroups.
31200 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.