Finite Group DatabasebetaFinite Group Databasebeta| order | 14196 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C132 ⋊ C3×C4 |
| Hall | C7⋊#10621730 ⋊ C3 |
| Hall | C7⋊#92789 ⋊ C4 |
| Sylow | C132 ⋊ ΓL(1,𝔽8)⋊C4 |
| Sylow | C7 ⋊ #14523149 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C132 | C3×C4 |
| prime radical | #20296924 | C2 |
| cosocle | C7×C13×D13 | C2×C3 |
| LCS | G ▷ C7×C132 | |
| UCS | C1 | |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,7,13^2|a^2=c,d^a=d^6,e^a=e^5,f^a=f^12,d^b=d^2,e^b=e^3,f^b=f^9,e^c=e^12133 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14196, 218);