Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C211 |
| direct product | #97×B(4,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×#120 |
| commutator | C24 | C23×C42 |
| Frattini, cosocle | C24×C4 | C25 |
| socle | C23 | C2×C4×#120 |
| prime radical | C22×B(4,𝔽2) | C2×C4 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C23×#97 ◁ G | |
| LECS | G ▷ C24×C4 ▷ C22 ▷ C1 | |
21780 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #442×B(4,𝔽2) |
| maximal normal subgroup of | #442×B(4,𝔽2) |
Past the SmallGroups library coverage — no SmallGroups id.