Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C2×#511932 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | #3027 |
| commutator, Frattini, cosocle | C2×#41 | C25 |
| socle | C22 | #32926 |
| LCS | G ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 ◁ C22×#131 ◁ G | |
| LECS | G ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1 | |
7186 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
106 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72236997, C2×#72237519, C2×#72237535 |
| maximal normal subgroup of | C2×#72236997, C2×#72237519, C2×#72237535 |
Past the SmallGroups library coverage — no SmallGroups id.