Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210×C4 |
| direct product | C2×#418909 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | H(3,𝔽4) |
| commutator, Frattini, cosocle | C23×C4 | C25 |
| socle | C23 | #2679 |
| LCS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
19095 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
148 conjugacy classes — view the full character table.
| maximal subgroup of | #72340597, #72340664, C2×#72226293, … |
| maximal normal subgroup of | #72340597, #72340664, C2×#72226293, … |
Past the SmallGroups library coverage — no SmallGroups id.