Finite Group DatabasebetaFinite Group Databasebeta| order | 11788 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #13132997⋊C7 |
| Fitting, socle, derived, Sylow | C421 ⋊ C4×C7 |
| Hall | C421⋊C7 ⋊ C4 |
| Hall | #13132997 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C421 | C4×C7 |
| prime radical | D421⋊C7 | C2 |
| cosocle | D421 | C2×C7 |
| LCS | G ▷ C421 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,2,421|a^2=c,d^a=d^29,d^b=d^370,d^c=d^42043 conjugacy classes — view the full character table.
| maximal subgroup of | (#13132997⋊C3)⋊C7, C3×#13132997⋊C7, C3⋊(#13132997⋊C7) |
| maximal normal subgroup of | (#13132997⋊C3)⋊C7, C3×#13132997⋊C7 |
| maximal quotient of | C3×#13132997⋊C7, C3⋊(#13132997⋊C7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11788, 8);