Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C2×#72237526 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | D4×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×#41 | C26 |
| LCS | G ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ C22×#576 ◁ G | |
| LECS | G ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1 | |
At least 7146 conjugacy classes of subgroups; only the 4464 normal subgroups are shown.
176 conjugacy classes — view the full character table.
| maximal subgroup of | #72313012, C2×#72237558, C2×#72240991 |
| maximal normal subgroup of | #72313012, C2×#72237558 |
Past the SmallGroups library coverage — no SmallGroups id.