Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C42 · Schur multiplier (H2) = C220×C4 |
| direct product | C2×C4×#14679 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25×C4 | C24 |
| commutator | C23 | C24×C42 |
| Frattini, cosocle | C25 | C26 |
| prime radical | C29 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C25×C4 ◁ G | |
| LECS | G ▷ C25 ▷ C1 | |
8189304 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72296169, C2×#72296177, C2×C4×#6342371 |
| maximal normal subgroup of | C2×#72296169, C2×#72296177, C2×C4×#6342371 |
Past the SmallGroups library coverage — no SmallGroups id.