Finite Group DatabasebetaFinite Group Databasebeta| order | 10848 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 4816896 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C3×C4×C113 |
| multiplicative | (ℤ/23608)ˣ, (ℤ/23835)ˣ, (ℤ/25424)ˣ, (ℤ/31780)ˣ, (ℤ/32688)ˣ, (ℤ/35412)ˣ, (ℤ/40860)ˣ, (ℤ/47670)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C3×C113 |
| socle, prime radical | C24×C3×C113 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
472 conjugacy classes of subgroups.
10848 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.