Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C222 |
| direct product | C2×#72240172 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C4 | C25 |
| commutator, Frattini, cosocle | C24 | C27 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C24 ▷ C1 | |
At least 7982 conjugacy classes of subgroups; only the 48744 normal subgroups are shown.
416 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#120×#525 |
| maximal normal subgroup of | C2×#120×#525 |
| maximal quotient of | C2×#72310675 |
Past the SmallGroups library coverage — no SmallGroups id.