Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C42 · Schur multiplier (H2) = C213×C42 |
| direct product | C22×C4×#418 |
| subgroup | G/H | |
|---|---|---|
| center | C24×C4 | C2×D4 |
| commutator | C4 | C24×C42 |
| Frattini, cosocle | C22×C4 | C26 |
| socle | C25 | C22×D4 |
| prime radical | C25×D4 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C4 ◁ C24×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
72365 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C4×#3003, C2×#72310639, C2×#72310631, … |
| maximal normal subgroup of | C22×C4×#3003, C2×#72310639, C2×#72310631, … |
Past the SmallGroups library coverage — no SmallGroups id.