Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C216 |
| direct product | C2×#72286057 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | #2403 |
| commutator | C22×C4 | C25×C4 |
| Frattini, cosocle | C23×C4 | C26 |
| socle | C22 | C4×#2403 |
| prime radical | C2×#6437463 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8 ◁ C24×C8 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
115308 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72317393 |
| maximal normal subgroup of | C2×#72317393 |
Past the SmallGroups library coverage — no SmallGroups id.