Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C42 · Schur multiplier (H2) = C214 |
| direct product | #97×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, cosocle | C22×C4 | C26 |
| commutator | C22 | C24×C42 |
| socle | C23 | C25×C4 |
| prime radical | C22×H(5,𝔽2) | C2×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
19795 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
340 conjugacy classes. The character table is too large to display.
| maximal subgroup of | H(5,𝔽2)×#442, #72313781, #97×B(4,𝔽2) |
| maximal normal subgroup of | H(5,𝔽2)×#442, #72313781, #97×B(4,𝔽2) |
| maximal quotient of | #72315568 |
Past the SmallGroups library coverage — no SmallGroups id.