Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#240064 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C25 |
| socle | C23 | C2×#394 |
| prime radical | C2×#60558 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C23×C42 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
7395 conjugacy classes of subgroups.
160 conjugacy classes — view the full character table.
| maximal subgroup of | #72213466, #72216104, C2×#72216088 |
| maximal normal subgroup of | #72213466, #72216104, C2×#72216088 |
Past the SmallGroups library coverage — no SmallGroups id.