Finite Group DatabasebetaFinite Group Databasebeta| order | 12404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D443 |
| unambiguous semidirect product | (D7×C443)⋊C2 |
| unambiguous semidirect product | (C7×D443)⋊C2 |
| unambiguous semidirect product | D3101⋊C2 |
| Fitting, socle, derived, Hall | C7×C443 ⋊ C22 |
| Sylow | C443 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D443 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C443 | C22 |
| LCS | G ▷ C7×C443 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
1115 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,𝔽7)×D443, C3×D7×D443, D21×D443, … |
| maximal normal subgroup of | AGL(1,𝔽7)×D443, C3×D7×D443 |
| maximal quotient of | C3×D7×D443, D21×D443, D7×D1329, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12404, 6);