Finite Group DatabasebetaFinite Group Databasebeta| order | 7357 |
| automorphism | ? |
| homology | Abelianization (H1) = C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C1051⋊C7 |
| Fitting, socle, derived, Sylow | C1051 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1051 | C7 |
| LCS | G ▷ C1051 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
7,1051|b^a=b^845157 conjugacy classes — view the full character table.
| maximal subgroup of | D1051⋊C7, C2×C1051⋊C7, (C1051⋊C3)⋊C7, … |
| maximal normal subgroup of | D1051⋊C7, C2×C1051⋊C7, (C1051⋊C3)⋊C7, … |
| maximal quotient of | C2×C1051⋊C7, C3×C1051⋊C7, C5×C1051⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7357, 1);