Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C216 |
| direct product | C2×#72250438 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C22×#120 |
| commutator | C22×C4 | C25×C4 |
| Frattini, cosocle | C23×C4 | C26 |
| prime radical | C23×#3109 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C24×C42 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
113768 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72311718 |
| maximal normal subgroup of | C2×#72311718 |
Past the SmallGroups library coverage — no SmallGroups id.