Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C28 · Schur multiplier (H2) = C227 |
| direct product | C2×#10586020 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C4 | C26 |
| commutator, Frattini, cosocle | C22 | C28 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C22 ▷ C1 | |
817801 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72249921, #72314842 |
| maximal normal subgroup of | C2×#72249921, #72314842 |
| maximal quotient of | C2×#72257036, C2×#72304329, C2×#72237366 |
Past the SmallGroups library coverage — no SmallGroups id.