Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | C2×#494695 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×#99 |
| commutator | C24 | C24×C4 |
| Frattini, cosocle | C22×D4 | C25 |
| prime radical | C2×#34980 | C2 |
| LCS | G ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C26 ◁ C25×D4 ◁ G | |
| LECS | G ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1 | |
25863 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | #72280573, C2×#72218077, #72286214 |
| maximal normal subgroup of | #72280573, C2×#72218077, #72286214 |
| maximal quotient of | #72280573, #72282838, #72285538, … |
Past the SmallGroups library coverage — no SmallGroups id.