Finite Group DatabasebetaFinite Group Databasebeta| order | 10668 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D21×D127 |
| unambiguous semidirect product | (C3×D127)⋊D7 |
| unambiguous semidirect product | (C7×D127)⋊D3 |
| Fitting, socle, derived, Hall | C3×C7×C127 ⋊ C22 |
| Hall | C7×C127 ⋊ C2×D3 |
| Hall | C3×C127 ⋊ C2×D7 |
| Sylow | C127 ⋊ C2×D21 |
| Hall | C3×C7 ⋊ C2×D127 |
| Sylow | C7 ⋊ D3×D127 |
| Sylow | C3 ⋊ D7×D127 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C127 | C22 |
| LCS | G ▷ C3×C7×C127 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
780 conjugacy classes — view the full character table.
| maximal subgroup of | D63×D127, #19128624⋊D3, #19128625⋊D3, … |
| maximal normal subgroup of | #19128624⋊D3, #19128625⋊D3, C3⋊AGL(1,𝔽7)×D127, … |
| maximal quotient of | D63×D127, C3×D21×D127, D381⋊D21, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10668, 59);