Finite Group DatabasebetaFinite Group Databasebeta| order | 6123 |
| isoclinism | isoclinic class of C157⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×C157⋊C3 |
| Fitting, socle, Hall | C13×C157 ⋊ C3 |
| derived, Sylow | C157 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C157⋊C3 |
| commutator, hypocenter | C157 | C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C157 | C3 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C13 | |
8 conjugacy classes of subgroups.
715 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C13×C157⋊C3, C13×D157⋊C3, D13×C157⋊C3, … |
| maximal normal subgroup of | C2×C13×C157⋊C3, C13×D157⋊C3, D13×C157⋊C3, … |
| maximal quotient of | C2×C13×C157⋊C3, C13×C157⋊C9, C3×C13×C157⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6123, 4);