Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
| direct product | C2×#7622635 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×#442 |
| commutator | C8 | C25×C4 |
| Frattini, cosocle | C2×C8 | C26 |
| socle | C22 | C22×#442 |
| prime radical | C22×#3414 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C24×C4 ◁ C22×#405 ◁ G | |
| LECS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
14949 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72286071, C2×#72307102, C2×#72307107 |
| maximal normal subgroup of | C2×#72286071, C2×#72307102, C2×#72307107 |
Past the SmallGroups library coverage — no SmallGroups id.