Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
| direct product | C2×#72224987 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×#2177 |
| commutator | C16 | C25×C4 |
| Frattini, cosocle | C2×C16 | C26 |
| prime radical | C2×#7625195 | C2 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×#41 ◁ C2×C4×#131 ◁ C2×#33326 ◁ G | |
| LECS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
19828 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72225087, C2×#72225101, C2×#72225018 |
| maximal normal subgroup of | C2×#72225087, C2×#72225101, C2×#72225018 |
| maximal quotient of | #72322589 |
Past the SmallGroups library coverage — no SmallGroups id.