Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | C2×#72211654 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C2×#127 |
| commutator | C2×C42 | C24×C4 |
| Frattini, cosocle | C22×C42 | C25 |
| socle | C24 | C2×#392 |
| prime radical | C22×#10012 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ C22×C43 ◁ G | |
| LECS | G ▷ C22×C42 ▷ C22 ▷ C1 | |
36740 conjugacy classes of subgroups.
272 conjugacy classes. The character table is too large to display.
| maximal normal subgroup of | #72218064 |
| maximal quotient of | C2×#72211666, C2×#72216677 |
Past the SmallGroups library coverage — no SmallGroups id.