Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C29 |
| direct product | C2×#105849 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22⋊#95 |
| commutator | C22×C4 | C22×C42 |
| Frattini, cosocle | C24×C4 | C24 |
| prime radical | C25×D4 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C25×C4 ◁ G | |
| LECS | G ▷ C24×C4 ▷ C22 ▷ C1 | |
21025 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | #72314430 |
| maximal normal subgroup of | #72314430 |
| maximal quotient of | C2×#72238685 |
Past the SmallGroups library coverage — no SmallGroups id.