Finite Group DatabasebetaFinite Group Databasebeta| order | 31200 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 17694720 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4×C5 |
| abelian | C2×C3×C42×C52×C13 |
| multiplicative | (ℤ/35563)ˣ, (ℤ/39955)ˣ, (ℤ/41075)ˣ, (ℤ/42575)ˣ, (ℤ/43175)ˣ, (ℤ/46475)ˣ, (ℤ/71126)ˣ, (ℤ/79910)ˣ, (ℤ/82150)ˣ, (ℤ/85150)ˣ, (ℤ/86350)ˣ, (ℤ/92950)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C23×C3×C52×C13 |
| socle, prime radical | C23×C3×C52×C13 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1728 conjugacy classes of subgroups.
31200 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.