Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
| direct product | C2×#72213160 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | #1619 |
| commutator, Frattini, cosocle | C22×C4×C8 | C24 |
| LCS | G ▷ C22×C4×C8 ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C24×C4 ◁ C23×C4×C8 ◁ G | |
| LECS | G ▷ C22×C4×C8 ▷ C22×C4 ▷ C2 ▷ C1 | |
16890 conjugacy classes of subgroups.
176 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72213209 |
| maximal normal subgroup of | #72217914 |
| maximal quotient of | #72213854 |
Past the SmallGroups library coverage — no SmallGroups id.