Finite Group DatabasebetaFinite Group Databasebeta| order | 29316 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C349 ⋊ C3×C4 |
| Hall | C7⋊#13063703 ⋊ C3 |
| Hall | C7×C349⋊C3 ⋊ C4 |
| Hall | C349⋊C3 ⋊ Dic7 |
| Sylow | C349 ⋊ C3×Dic7 |
| Sylow | C7 ⋊ #13063703⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C349 | C3×C4 |
| prime radical | C7×D349⋊C3 | C2 |
| cosocle | C7×D349 | C2×C3 |
| LCS | G ▷ C7×C349 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2443 |
Polycyclic presentation:
2,3,2,7,349|a^2=c,d^a=d^6,e^a=e^136,e^b=e^122,e^c=e^348233 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29316, 36);