Finite Group DatabasebetaFinite Group Databasebeta| order | 6162 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#15690493 |
| Fitting, socle, Hall | C2×C13×C79 ⋊ C3 |
| derived, Hall | C13×C79 ⋊ C2×C3 |
| Hall | C2×C79 ⋊ C13⋊C3 |
| Sylow | C79 ⋊ C2×C13⋊C3 |
| Hall | C2×C13 ⋊ C79⋊C3 |
| Sylow | C13 ⋊ C2×C79⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #15690493 |
| commutator, hypocenter | C13×C79 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C13×C79 | C3 |
| LCS | G ▷ C13×C79 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
690 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#15690493, #27134498, #27134502, … |
| maximal normal subgroup of | C4×#15690493, #27134498, #27134502, … |
| maximal quotient of | C4×#15690493, C22×#15690493, C2×#22604455, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6162, 5);