Finite Group DatabasebetaFinite Group Databasebeta| order | 7876 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic179 |
| unambiguous semidirect product | C179⋊(C4×C11) |
| derived, Sylow | C179 ⋊ C4×C11 |
| Hall | C11×C179 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D179 |
| commutator, hypocenter | C179 | C4×C11 |
| Frattini | C2 | C11×D179 |
| Fitting, socle | C2×C11×C179 | C2 |
| LCS | G ▷ C179 | |
| UCS | C1 ◁ C2×C11 | |
12 conjugacy classes of subgroups.
2002 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C11×Dic179, C11×Dic537 |
| maximal normal subgroup of | C3×C11×Dic179 |
| maximal quotient of | C3×C11×Dic179, C11×Dic537 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7876, 3);