Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C213 |
| direct product | C2×#394133 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #14715 |
| commutator, Frattini, cosocle | C23×C4 | C25 |
| LCS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
At least 6491 conjugacy classes of subgroups; only the 1629 normal subgroups are shown.
130 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72216203, C2×#72216192, C2×#72216013, … |
| maximal normal subgroup of | C2×#72216203, C2×#72216192, C2×#72216013, … |
| maximal quotient of | C2×#72252141, #72338255 |
Past the SmallGroups library coverage — no SmallGroups id.