Finite Group DatabasebetaFinite Group Databasebeta| order | 31200 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 4423680 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C5 |
| abelian | C22×C3×C52×C8×C13 |
| multiplicative | (ℤ/35629)ˣ, (ℤ/37597)ˣ, (ℤ/40117)ˣ, (ℤ/48339)ˣ, (ℤ/48453)ˣ, (ℤ/51579)ˣ, (ℤ/64604)ˣ, (ℤ/71258)ˣ, (ℤ/75194)ˣ, (ℤ/80234)ˣ, (ℤ/96678)ˣ, (ℤ/96906)ˣ, (ℤ/103158)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C23×C3×C52×C13 |
| socle, prime radical | C23×C3×C52×C13 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1216 conjugacy classes of subgroups.
31200 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.