Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214×C4 |
| direct product | C22×#17595 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C22×C22⋊C4 |
| commutator | C2×C4 | C25×C4 |
| Frattini, cosocle | C22×C4 | C26 |
| prime radical | C23×#532 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C24×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
41645 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#6346637, C2×#72249998, C2×#72250438, … |
| maximal normal subgroup of | C22×#6346637, C2×#72249998, C2×#72250438, … |
| maximal quotient of | C2×#72264297, C2×#72308146, C2×#72264565, … |
Past the SmallGroups library coverage — no SmallGroups id.