Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C219 |
| direct product | C2×#72215721 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×#52004 |
| commutator, Frattini, cosocle | C22×C4 | C27 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
At least 8865 conjugacy classes of subgroups; only the 32264 normal subgroups are shown.
212 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72216611, C2×#72215764, C2×#72216359 |
| maximal normal subgroup of | C2×#72216611, C2×#72215764, C2×#72216359 |
Past the SmallGroups library coverage — no SmallGroups id.