Finite Group DatabasebetaFinite Group Databasebeta| order | 34006 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C347 · Schur multiplier (H2) = C1 |
| direct product | C7×D7×C347 |
| unambiguous semidirect product | C7⋊(C2×C7×C347) |
| Fitting, socle, Hall | C72×C347 ⋊ C2 |
| derived | C7 ⋊ C2×C7×C347 |
| Sylow | C72 ⋊ C2×C347 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C347 | D7 |
| commutator, cosocle, hypocenter | C7 | C2×C7×C347 |
| Frattini | C1 | G |
| Fitting, socle | C72×C347 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C7×C347 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4858 |
12145 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34006, 7);