Finite Group DatabasebetaFinite Group Databasebeta| order | 6123 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C157 ⋊ C3 |
| Sylow | C157 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ C157⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C157 | C3 |
| LCS | G ▷ C13×C157 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
3,13,157|b^a=b^3,c^a=c^12683 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20259404, #27133641, #27133645, … |
| maximal normal subgroup of | C2×#20259404, #27133641, #27133645, … |
| maximal quotient of | C2×#20259404, #32913541, C3×#20259404, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6123, 5);