Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C216 |
| direct product | C2×C4×#23895 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | #2403 |
| commutator | C24 | C25×C4 |
| Frattini, cosocle | C25 | C26 |
| socle | C23 | C2×#2403 |
| prime radical | C22×#23895 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C25×C4 ◁ G | |
| LECS | G ▷ C25 ▷ C2 ▷ C1 | |
139540 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
320 conjugacy classes. The character table is too large to display.
| maximal quotient of | C2×C4×#245225 |
Past the SmallGroups library coverage — no SmallGroups id.