Finite Group DatabasebetaFinite Group Databasebeta| order | 31320 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 338688 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C5×C27×C29 |
| multiplicative | (ℤ/47967)ˣ, (ℤ/51711)ˣ, (ℤ/52569)ˣ, (ℤ/63956)ˣ, (ℤ/68948)ˣ, (ℤ/95934)ˣ, (ℤ/103422)ˣ, (ℤ/105138)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C9 | C23×C3×C5×C29 |
| socle, prime radical | C23×C3×C5×C29 | C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
256 conjugacy classes of subgroups.
31320 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.