Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C4 |
| direct product | C2×#233521 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C2×#127 |
| commutator, Frattini, cosocle | C2×C42 | C25 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C23×C42 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
16169 conjugacy classes of subgroups.
136 conjugacy classes — view the full character table.
| maximal subgroup of | #72214837, #72217845, #72226652, … |
| maximal normal subgroup of | #72214837, #72217845, #72226652, … |
| maximal quotient of | C2×#72211642, C2×#72211656 |
Past the SmallGroups library coverage — no SmallGroups id.