Finite Group DatabasebetaFinite Group Databasebeta| order | 14196 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C132 ⋊ C3×C4 |
| Hall | C7×C13×Dic13 ⋊ C3 |
| Hall | C7⋊#92789 ⋊ C4 |
| Hall | C13×Dic13 ⋊ ΓL(1,𝔽8) |
| Sylow | C132 ⋊ C4×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ #14523131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #20296924 |
| commutator, hypocenter | C7×C132 | C3×C4 |
| Fitting, socle, cosocle | C2×C7×C132 | C2×C3 |
| prime radical | C2×C7⋊#92789 | C2 |
| LCS | G ▷ C7×C132 | |
| UCS | C1 ◁ C2 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,13^2,2|a^2=f,d^a=d^12,c^b=c^2,d^b=d^3,e^b=e^9496 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14196, 124);