Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C217 |
| direct product | C2×#72218460 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | #32898 |
| commutator, Frattini, cosocle | C22×D4 | C26 |
| socle | C22 | C2×#32898 |
| LCS | G ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C23×C4 ◁ C24×#41 ◁ G | |
| LECS | G ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1 | |
At least 14225 conjugacy classes of subgroups; only the 6592 normal subgroups are shown.
212 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72238006, C2×#72218487, C2×#72233466, … |
| maximal normal subgroup of | C2×#72238006, C2×#72233466, C2×#72317393 |
| automorphism group of | #2112, #2150 |
Past the SmallGroups library coverage — no SmallGroups id.