Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C217 |
| direct product | C2×#72234146 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×B(4,𝔽2) |
| commutator, Frattini, cosocle | C22×D4 | C26 |
| LCS | G ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C23×D4 ◁ C23×H(5,𝔽2) ◁ G | |
| LECS | G ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1 | |
At least 6688 conjugacy classes of subgroups; only the 5168 normal subgroups are shown.
200 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72236721, C2×#72236986, C2×#72246533 |
| maximal normal subgroup of | C2×#72236721, C2×#72236986 |
Past the SmallGroups library coverage — no SmallGroups id.