Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C212 |
| direct product | C2×#185022 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C22×C22⋊C4 |
| commutator | C22×C4 | C24×C4 |
| Frattini, cosocle | C23×C4 | C25 |
| prime radical | C23×#525 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C26×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
43857 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | #72261015, #72261036, #72261172 |
| maximal normal subgroup of | #72261015, #72261036, #72261172 |
| maximal quotient of | #72261998 |
Past the SmallGroups library coverage — no SmallGroups id.