Finite Group DatabasebetaFinite Group Databasebeta| order | 7678 |
| automorphism | Aut(G) order 13359720 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3839 |
| unambiguous semidirect product | C11⋊D349 |
| unambiguous semidirect product | C349⋊D11 |
| Fitting, socle, derived, Hall | C11×C349 ⋊ C2 |
| Sylow | C349 ⋊ D11 |
| Sylow | C11 ⋊ D349 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C349 | C2 |
| LCS | G ▷ C11×C349 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,11,349|b^a=b^10,c^a=c^3481921 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×D349, C2×D3839, C3×D3839, … |
| maximal normal subgroup of | D11×D349, C2×D3839, C3×D3839, … |
| maximal quotient of | Dic3839, C2×D3839, C3×D3839, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7678, 3);