Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C27×C4 · Schur multiplier (H2) = C229 |
| direct product | C26×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C28 | C22 |
| commutator | C2 | C27×C4 |
| Frattini, cosocle | C22 | C28 |
| prime radical | C29 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C28 ◁ G | |
| LECS | G ▷ C22 ▷ C1 | |
5293909 conjugacy classes of subgroups.
| transitive degree | μt(G) = 512 |
640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72268589, C26×#120, C22×C22⋊C4×#120, … |
| maximal normal subgroup of | #72268589, C26×#120, C22×C22⋊C4×#120, … |
| maximal quotient of | C24×D4×C22⋊C4, C27×C22⋊C4, C23×#34171, … |
Past the SmallGroups library coverage — no SmallGroups id.