Finite Group DatabasebetaFinite Group Databasebeta| order | 8144 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C509 · Schur multiplier (H2) = C2 |
| direct product | C4⋊C4×C509 |
| unambiguous semidirect product | C4⋊(C4×C509) |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C509 | C22 |
| commutator | C2 | C2×C4×C509 |
| Frattini, cosocle | C22 | C22×C509 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C509 ◁ G | |
26 conjugacy classes of subgroups.
5090 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8144, 4);