Finite Group DatabasebetaFinite Group Databasebeta| order | 27344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×#20292020 |
| unambiguous semidirect product | D1709⋊(C2×C4) |
| Fitting, socle | C22×C1709 ⋊ C4 |
| derived, Sylow | C1709 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #20292020 |
| commutator, hypocenter | C1709 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C1709 | C4 |
| prime radical | C22×D1709 | C2 |
| cosocle | D1709 | C23 |
| LCS | G ▷ C1709 | |
| UCS | C1 ◁ C22 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6836 |
1724 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27344, 51);