Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C220 |
| direct product | C2×#72307949 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×#120 |
| commutator, Frattini, cosocle | C22×C4 | C27 |
| socle | C23 | C23×#120 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C24×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
At least 16578 conjugacy classes of subgroups; only the 39544 normal subgroups are shown.
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72310675 |
| maximal normal subgroup of | C2×#72310675 |
| maximal quotient of | C2×#72308187 |
Past the SmallGroups library coverage — no SmallGroups id.