Finite Group DatabasebetaFinite Group Databasebeta| order | 6996 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C11⋊#6157) |
| unambiguous semidirect product | C11⋊(C3⋊#6157) |
| Fitting, socle, derived, Hall | C3×C11×C53 ⋊ C4 |
| Hall | C11×C53 ⋊ Dic3 |
| Hall | C3×C53 ⋊ Dic11 |
| Sylow | C53 ⋊ Dic33 |
| Hall | C3×C11 ⋊ #6157 |
| Sylow | C11 ⋊ C3⋊#6157 |
| Sylow | C3 ⋊ C11⋊#6157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C11×C53 | C4 |
| LCS | G ▷ C3×C11×C53 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,11,53|a^2=b,c^a=c^2,d^a=d^10,e^a=e^30,e^b=e^52465 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6996, 15);