Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C218×C4 |
| direct product | C22×#34593 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C4 | C24 |
| commutator, Frattini, cosocle | C23 | C27 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
112149 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#7718113, C22×#7758045, C22×#7629437, … |
| maximal normal subgroup of | C22×#7718113, C22×#7758045, C22×#7629437, … |
| maximal quotient of | C22×#607767, C2×#72280516, C2×#72280482, … |
Past the SmallGroups library coverage — no SmallGroups id.