Finite Group DatabasebetaFinite Group Databasebeta| order | 8144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×#14523266 |
| unambiguous semidirect product | D509⋊(C2×C4) |
| Fitting, socle | C22×C509 ⋊ C4 |
| derived, Sylow | C509 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #14523266 |
| commutator, hypocenter | C509 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C509 | C4 |
| LCS | G ▷ C509 | |
| UCS | C1 ◁ C22 | |
54 conjugacy classes of subgroups.
524 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8144, 51);