Finite Group DatabasebetaFinite Group Databasebeta| order | 7124 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D13×D137 |
| unambiguous semidirect product | (D13×C137)⋊C2 |
| unambiguous semidirect product | (C13×D137)⋊C2 |
| unambiguous semidirect product | D1781⋊C2 |
| Fitting, socle, derived, Hall | C13×C137 ⋊ C22 |
| Sylow | C137 ⋊ C2×D13 |
| Sylow | C13 ⋊ C2×D137 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C137 | C22 |
| LCS | G ▷ C13×C137 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
560 conjugacy classes — view the full character table.
| maximal subgroup of | D13⋊C3×D137, C3×D13×D137, D39×D137, … |
| maximal normal subgroup of | D13⋊C3×D137, C3×D13×D137, C5×D13×D137 |
| maximal quotient of | C3×D13×D137, D39×D137, D13×D411, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7124, 12);