Finite Group DatabasebetaFinite Group Databasebeta| order | 16000 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 292552704000 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4×C53 |
| abelian | C22×C4×C53×C8 |
| multiplicative | (ℤ/33825)ˣ, (ℤ/45100)ˣ, (ℤ/67650)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4 | C24×C53 |
| socle, prime radical | C24×C53 | C2×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
24320 conjugacy classes of subgroups.
16000 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C4×C53×C16, C22×C53×C82, C2×C42×C53×C8, … |
| maximal normal subgroup of | C22×C4×C53×C16, C22×C53×C82, C2×C42×C53×C8, … |
| maximal quotient of | C22×C4×C53×C16, C22×C53×C82, C2×C42×C53×C8, … |
Past the SmallGroups library coverage — no SmallGroups id.