Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C213 |
| direct product | C2×#72212208 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C23×Q8 | C25 |
| prime radical | C24×2−1+4 | C22 |
| LCS | G ▷ C23×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C26 ◁ C25×Q8 ◁ G | |
| LECS | G ▷ C23×Q8 ▷ C22 ▷ C2 ▷ C1 | |
141522 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | #72267040, #72267488 |
| maximal normal subgroup of | #72267040, #72267488 |
Past the SmallGroups library coverage — no SmallGroups id.