Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C219 |
| direct product | C2×#10584288 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C24×D4 |
| commutator, Frattini, cosocle | C2×C4 | C27 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C2×#3481 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
At least 6609 conjugacy classes of subgroups; only the 31709 normal subgroups are shown.
178 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72231596, C2×#72231701, C2×#72231699 |
| maximal normal subgroup of | C2×#72231596, C2×#72231701, C2×#72231699 |
Past the SmallGroups library coverage — no SmallGroups id.