Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C4 · Schur multiplier (H2) = C220 |
| direct product | D4×#3573 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C26 |
| commutator, socle | C22 | C26×C4 |
| Frattini, cosocle | C2×C4 | C27 |
| prime radical | D4×#585 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Only the 60207 normal subgroups are shown; non-normal subgroups are omitted.
340 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72287288, D4×#21483, #72343190 |
| maximal normal subgroup of | #72287288, D4×#21483, #72343190 |
| maximal quotient of | #72287288, #72320295 |
Past the SmallGroups library coverage — no SmallGroups id.