Finite Group DatabasebetaFinite Group Databasebeta| order | 7436 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C13 |
| unambiguous semidirect product | C11⋊#10621725 |
| derived, Hall | C11×C132 ⋊ C4 |
| Sylow | C132 ⋊ Dic11 |
| Sylow | C11 ⋊ #10621725 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊(C13⋊D13) |
| commutator, hypocenter | C11×C132 | C4 |
| Fitting, socle | C2×C11×C132 | C2 |
| LCS | G ▷ C11×C132 | |
| UCS | C1 ◁ C2 | |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2,11,13^2,2|a^2=e,b^a=b^10,c^a=c^12,d^a=d^121862 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7436, 17);