Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C2×#500772 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C22×D4 | C25 |
| prime radical | C2×#13343 | C2 |
| LCS | G ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C23×C4 ◁ C22×C4×D4 ◁ G | |
| LECS | G ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1 | |
8508 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #72312927, C2×#72312364, C2×#72312792 |
| maximal normal subgroup of | #72312927, C2×#72312364, C2×#72312792 |
Past the SmallGroups library coverage — no SmallGroups id.