Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C4 · Schur multiplier (H2) = C220 |
| direct product | C2×C4×#3585 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C23×D4 |
| commutator | C4 | C26×C4 |
| Frattini, cosocle | C2×C4 | C27 |
| socle | C23 | C24×D4 |
| prime radical | C22×#3585 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C4×#41 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
111773 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72257837, C2×C4×#23882, #72315337, … |
| maximal normal subgroup of | #72257837, C2×C4×#23882, #72315337, … |
| maximal quotient of | C2×#72256941 |
Past the SmallGroups library coverage — no SmallGroups id.