Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C212×C4 |
| direct product | C2×#7504005 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C23×D4 |
| commutator, Frattini, cosocle | C22×C4 | C26 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C2×C42×D4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
19641 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
148 conjugacy classes — view the full character table.
| maximal subgroup of | #72265530, #72307476, C2×#72256885, … |
| maximal normal subgroup of | #72265530, #72307476, C2×#72256885, … |
Past the SmallGroups library coverage — no SmallGroups id.