Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C4 · Schur multiplier (H2) = C220 |
| direct product | C22×C4×#534 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C4 | C24 |
| commutator | C22 | C26×C4 |
| Frattini, cosocle | C23 | C27 |
| prime radical | C23×#534 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
155069 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×#7675495, C22×#7763450, C22×C4×#3543, … |
| maximal normal subgroup of | C22×#7675495, C22×#7763450, C22×C4×#3543, … |
| maximal quotient of | C22×#523233, C22×C4×#2403, C22×C4×#2410, … |
Past the SmallGroups library coverage — no SmallGroups id.