Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C216 |
| direct product | C22×#23391 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C26 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C25 ◁ C26×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
98589 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72231796, C22×#6437510, C2×#72239546, … |
| maximal normal subgroup of | C2×#72231796, C22×#6437510, C2×#72239546, … |
| maximal quotient of | C2×#72237123, #72305075, C2×#72249980, … |
Past the SmallGroups library coverage — no SmallGroups id.