Finite Group DatabasebetaFinite Group Databasebeta| order | 23904 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 84639744 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C23×C32×C4×C83 |
| multiplicative | (ℤ/45591)ˣ, (ℤ/51896)ˣ, (ℤ/52395)ˣ, (ℤ/52605)ˣ, (ℤ/55832)ˣ, (ℤ/55888)ˣ, (ℤ/60788)ˣ, (ℤ/69860)ˣ, (ℤ/71784)ˣ, (ℤ/71856)ˣ, (ℤ/77844)ˣ, (ℤ/78156)ˣ, (ℤ/83748)ˣ, (ℤ/89820)ˣ, (ℤ/91182)ˣ, (ℤ/104790)ˣ, (ℤ/105210)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C32×C83 |
| socle, prime radical | C24×C32×C83 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1416 conjugacy classes of subgroups.
23904 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.