Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 5637144576 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C46 |
| abelian | C43×C32 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C23×C16 | C24 |
| socle, prime radical | C24 | C23×C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C23×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
6024 conjugacy classes of subgroups.
2048 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×C64, C42×C8×C32, C2×C43×C32, … |
| maximal normal subgroup of | C43×C64, C42×C8×C32, C2×C43×C32, … |
| maximal quotient of | C43×C64, C42×C8×C32, C2×C43×C32, … |
Past the SmallGroups library coverage — no SmallGroups id.