Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C217 |
| direct product | C2×#72214599 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | #2846 |
| commutator, Frattini, cosocle | C25 | C26 |
| socle | C23 | C2×#2846 |
| LCS | G ▷ C25 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C25×C4 ◁ G | |
| LECS | G ▷ C25 ▷ C22 ▷ C1 | |
Only the 6632 normal subgroups are shown; non-normal subgroups are omitted.
236 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72238006, C2×#72214923, C2×#72215542, … |
| maximal normal subgroup of | C2×#72238006, C2×#72214923, C2×#72233466 |
| automorphism group of | C2×C22⋊C16, C2×C4⋊C16 |
Past the SmallGroups library coverage — no SmallGroups id.