Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211×C4 |
| direct product | C2×#72216619 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C2×#127 |
| commutator | C2×C42 | C24×C4 |
| Frattini, cosocle | C22×C42 | C25 |
| socle | C24 | C2×#392 |
| prime radical | C23×#2397 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ C24×C42 ◁ G | |
| LECS | G ▷ C22×C42 ▷ C22 ▷ C1 | |
128472 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
272 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72303335 |
| maximal normal subgroup of | #72303335 |
| maximal quotient of | #72303335 |
Past the SmallGroups library coverage — no SmallGroups id.