Finite Group DatabasebetaFinite Group Databasebeta| order | 34006 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊D2429 |
| unambiguous semidirect product | C347⋊(C7⋊D7) |
| Fitting, socle, derived, Hall | C72×C347 ⋊ C2 |
| Sylow | C347 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ D347 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C347 | C2 |
| LCS | G ▷ C72×C347 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17003 |
Polycyclic presentation:
2,7^2,347|b^a=b^6,c^a=c^6,d^a=d^3468503 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34006, 10);