Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213×C4 |
| direct product | C22×#31076 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | H(3,𝔽4) |
| commutator, Frattini, cosocle | C22×C4 | C26 |
| socle | C23 | #2679 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
31329 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
160 conjugacy classes — view the full character table.
| derived subgroup of | #72257980, #72267242 |
| Fitting subgroup of | #72257980 |
| maximal subgroup of | #72257980, #72258244 |
| maximal normal subgroup of | #72257980, #72258244 |
| maximal quotient of | #72258228 |
Past the SmallGroups library coverage — no SmallGroups id.