Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C217 |
| direct product | C2×#72251110 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×#1790 |
| commutator | C2×D4 | C25×C4 |
| Frattini, cosocle | C22×D4 | C26 |
| prime radical | C2×#10586564 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×D4 ◁ C23×H(5,𝔽2) ◁ G | |
| LECS | G ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1 | |
Only the 14776 normal subgroups are shown; non-normal subgroups are omitted.
260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72256706 |
| maximal normal subgroup of | #72256706 |
| maximal quotient of | #72263700 |
Past the SmallGroups library coverage — no SmallGroups id.