Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#111959 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #1438 |
| commutator | C23×C4 | C23×C4 |
| Frattini, cosocle | C24×C4 | C24 |
| prime radical | C2×#35050 | C2 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C25×C4 ◁ G | |
| LECS | G ▷ C24×C4 ▷ C22 ▷ C1 | |
12655 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72260421, #72261193, #72262021, … |
| maximal normal subgroup of | C2×#72260421, #72261193, #72262021, … |
Past the SmallGroups library coverage — no SmallGroups id.