Finite Group DatabasebetaFinite Group Databasebeta| order | 11788 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D421 |
| unambiguous semidirect product | (D7×C421)⋊C2 |
| unambiguous semidirect product | (C7×D421)⋊C2 |
| unambiguous semidirect product | D2947⋊C2 |
| Fitting, socle, derived, Hall | C7×C421 ⋊ C22 |
| Sylow | C421 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D421 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C421 | C22 |
| LCS | G ▷ C7×C421 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
1060 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31799082⋊C2, #31799081⋊C2, AGL(1,𝔽7)×D421, … |
| maximal normal subgroup of | #31799082⋊C2, #31799081⋊C2, AGL(1,𝔽7)×D421, … |
| maximal quotient of | C3×D7×D421, D21×D421, D7×D1263, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11788, 13);