Finite Group DatabasebetaFinite Group Databasebeta| order | 34174 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D2441 |
| unambiguous semidirect product | C2441⋊(C2×C7) |
| Fitting, socle, Hall | C7×C2441 ⋊ C2 |
| derived, Sylow | C2441 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D2441 |
| commutator, cosocle, hypocenter | C2441 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C2441 | C2 |
| LCS | G ▷ C2441 | |
| UCS | C1 ◁ C7 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17087 |
8554 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34174, 2);