Finite Group DatabasebetaFinite Group Databasebeta| order | 10040 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 168000 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C5×C251 |
| multiplicative | (ℤ/16599)ˣ, (ℤ/22132)ˣ, (ℤ/33198)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
64 conjugacy classes of subgroups.
10040 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C4×C5×C251, C24×C5×C251, C23×C3×C5×C251 |
| maximal normal subgroup of | C22×C4×C5×C251, C24×C5×C251, C23×C3×C5×C251 |
| maximal quotient of | C22×C4×C5×C251, C24×C5×C251, C23×C3×C5×C251 |
Past the SmallGroups library coverage — no SmallGroups id.