Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C27×C4 |
| direct product | C4×#139750 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | #9495 |
| commutator | C25 | C22×C42 |
| Frattini, cosocle | C24×D4 | C24 |
| socle | C22 | C2×#9495 |
| prime radical | C2×#23900 | C22 |
| LCS | G ▷ C25 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C4×D4 ◁ G | |
| LECS | G ▷ C24×D4 ▷ C23 ▷ C2 ▷ C1 | |
17923 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
164 conjugacy classes — view the full character table.
| maximal subgroup of | C4×B(5,𝔽2), C4×#72215879 |
| maximal normal subgroup of | C4×B(5,𝔽2) |
Past the SmallGroups library coverage — no SmallGroups id.