Finite Group DatabasebetaFinite Group Databasebeta| order | 7124 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#10587739 |
| Fitting, socle, Hall | C13×C137 ⋊ C4 |
| derived, Sylow | C137 ⋊ C4×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | #10587739 |
| commutator, hypocenter | C137 | C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C137 | C4 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C13 | |
12 conjugacy classes of subgroups.
494 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7124, 6);