Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C221 |
| direct product | C22×#6346637 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C22×#120 |
| commutator, Frattini, cosocle | C22×C4 | C27 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C24×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
518384 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 |
| maximal quotient of | C2×#72308187, C2×#72311718 |
| automorphism group of | #7110, #7111, #7126, … |
Past the SmallGroups library coverage — no SmallGroups id.