Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C221 |
| direct product | C2×#10574854 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#120 |
| commutator, Frattini, cosocle | C2×C4 | C27 |
| socle | C22 | C23×#120 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C23×#41 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Only the 38405 normal subgroups are shown; non-normal subgroups are omitted.
232 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72237528, #72312222, #72313305, … |
| maximal normal subgroup of | C2×#72237528, #72312222, #72313305, … |
| maximal quotient of | #72313758 |
Past the SmallGroups library coverage — no SmallGroups id.