Finite Group DatabasebetaFinite Group Databasebeta| order | 23534 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C1681 · Schur multiplier (H2) = C1 |
| direct product | D7×C1681 |
| unambiguous semidirect product | C7⋊(C2×C1681) |
| Fitting, Hall | C7×C1681 ⋊ C2 |
| derived, Sylow | C7 ⋊ C2×C1681 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1681 | D7 |
| commutator, hypocenter | C7 | C2×C1681 |
| Frattini | C41 | D7×C41 |
| Fitting | C7×C1681 | C2 |
| socle, cosocle | C7×C41 | C2×C41 |
| prime radical | D7×C41 | C41 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C1681 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11767 |
8405 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23534, 2);