Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C213 |
| direct product | C4×#14724 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C4 | C24 |
| commutator | C24 | C24×C4 |
| Frattini, cosocle | C25 | C25 |
| prime radical | C25×D4 | C22 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C25 ▷ C1 | |
63297 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | #72339930, #72339939, #72339940, … |
| maximal normal subgroup of | #72339930, #72339939, #72339940, … |
| maximal quotient of | C4×#154094 |
Past the SmallGroups library coverage — no SmallGroups id.