Finite Group DatabasebetaFinite Group Databasebeta| order | 7756 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#11764308 |
| Fitting, socle, Hall | C7×C277 ⋊ C4 |
| derived, Sylow | C277 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #11764308 |
| commutator, hypocenter | C277 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C277 | C4 |
| LCS | G ▷ C277 | |
| UCS | C1 ◁ C7 | |
12 conjugacy classes of subgroups.
511 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#11764308⋊C3, #37551637, #37551638, … |
| maximal normal subgroup of | C7×#11764308⋊C3, #37551637, #37551638, … |
| maximal quotient of | C3×C7×#11764308, C7×C3⋊#11764308 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7756, 6);