Finite Group DatabasebetaFinite Group Databasebeta| order | 12796 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D457 |
| unambiguous semidirect product | (D7×C457)⋊C2 |
| unambiguous semidirect product | (C7×D457)⋊C2 |
| unambiguous semidirect product | D3199⋊C2 |
| Fitting, socle, derived, Hall | C7×C457 ⋊ C22 |
| Sylow | C457 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D457 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C457 | C22 |
| LCS | G ▷ C7×C457 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
1150 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34063056⋊C2, #34063057⋊C2, AGL(1,𝔽7)×D457, … |
| maximal normal subgroup of | #34063056⋊C2, #34063057⋊C2, AGL(1,𝔽7)×D457, … |
| maximal quotient of | C3×D7×D457, D21×D457, D7×D1371, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12796, 8);