Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C213×C4 |
| direct product | C2×#6343376 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×C22⋊C4 |
| commutator | C2×C4 | C25×C4 |
| Frattini, cosocle | C22×C4 | C26 |
| socle | C23 | C23×C22⋊C4 |
| prime radical | C22×#3444 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C24×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
29269 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72307976, C2×#72307970 |
| maximal normal subgroup of | C2×#72307976, C2×#72307970 |
| maximal quotient of | C2×#72308146, C2×#72311704 |
Past the SmallGroups library coverage — no SmallGroups id.