Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C2×#497324 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | D4×#99 |
| commutator | C22×C4 | C24×C4 |
| Frattini, cosocle | C2×#41 | C25 |
| prime radical | C2×#61050 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ C22×#577 ◁ G | |
| LECS | G ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1 | |
8209 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
118 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72237521, C2×#72237525, C2×#72237542 |
| maximal normal subgroup of | C2×#72237521, C2×#72237525, C2×#72237542 |
Past the SmallGroups library coverage — no SmallGroups id.