Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C220 |
| direct product | C22×#61049 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C27 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C22×#525 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
126173 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
232 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#10576108, C22×#10576928, C2×#72238726, … |
| maximal normal subgroup of | C22×#10576108, C22×#10576928, C2×#72238726, … |
| maximal quotient of | C22×D8×#120, C22×#6573477, C22×#6576546, … |
Past the SmallGroups library coverage — no SmallGroups id.