Finite Group DatabasebetaFinite Group Databasebeta| order | 6223 |
| automorphism | ? |
| homology | Abelianization (H1) = C72 · Schur multiplier (H2) = C7 |
| direct product | C7×C127⋊C7 |
| unambiguous semidirect product | C127⋊C72 |
| unambiguous semidirect product | (C7×C127)⋊C7 |
| Fitting, socle | C7×C127 ⋊ C7 |
| derived, Sylow | C127 ⋊ C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C127⋊C7 |
| commutator, hypocenter | C127 | C72 |
| Frattini | C1 | G |
| Fitting, socle | C7×C127 | C7 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C7 | |
20 conjugacy classes of subgroups.
175 conjugacy classes — view the full character table.
| maximal subgroup of | C7×D127⋊C7, C7⋊(D127⋊C7), D7×C127⋊C7, … |
| maximal normal subgroup of | C7×D127⋊C7, C7⋊(D127⋊C7), D7×C127⋊C7, … |
| maximal quotient of | C2×C7×C127⋊C7, C3×C7×C127⋊C7, C5×C7×C127⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6223, 3);