Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C42 · Schur multiplier (H2) = C216 |
| direct product | C22×#20338 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×C42 |
| commutator | C4 | C24×C42 |
| Frattini, cosocle | C22×C4 | C26 |
| socle | C23 | C22×#95 |
| prime radical | C24×#41 | C22 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
77177 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×#6431743, #72302364, C2×#72239641, … |
| maximal normal subgroup of | C22×#6431743, #72302364, C2×#72239641, … |
Past the SmallGroups library coverage — no SmallGroups id.