Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C28 · Schur multiplier (H2) = C227 |
| direct product | C22×#62812 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C4 | C25 |
| commutator, Frattini, cosocle | C22 | C28 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C22 ▷ C1 | |
827517 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×#6346637, C22×#10586740, #72307023, … |
| maximal normal subgroup of | C22×#6346637, C22×#10586740, #72307023, … |
| maximal quotient of | C22×#7671575, C2×#72308109, C2×#72311691 |
Past the SmallGroups library coverage — no SmallGroups id.