Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C213 |
| direct product | C2×#357561 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | #392 |
| commutator | C22×C4 | C24×C4 |
| Frattini, cosocle | C23×C4 | C25 |
| socle | C23 | C2×#392 |
| prime radical | C22×#3449 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C25×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
41849 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | #72314617, #72314672, #72314711, … |
| maximal normal subgroup of | #72314617, #72314672, #72314711, … |
Past the SmallGroups library coverage — no SmallGroups id.