Finite Group DatabasebetaFinite Group Databasebeta| order | 6916 |
| automorphism | Aut(G) order 4481568 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3458 |
| direct product | C2×D1729 |
| unambiguous semidirect product | (C2×C7)⋊D247 |
| unambiguous semidirect product | (C2×C13)⋊D133 |
| unambiguous semidirect product | (C2×C19)⋊D91 |
| Fitting, socle | C2×C7×C13×C19 ⋊ C2 |
| derived, Hall | C7×C13×C19 ⋊ C22 |
| Hall | C13×C19 ⋊ C2×D7 |
| Hall | C7×C19 ⋊ C2×D13 |
| Hall | C7×C13 ⋊ C2×D19 |
| Sylow | C19 ⋊ C2×D91 |
| Sylow | C13 ⋊ C2×D133 |
| Sylow | C7 ⋊ C2×D247 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1729 |
| commutator, hypocenter | C7×C13×C19 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C13×C19 | C2 |
| LCS | G ▷ C7×C13×C19 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
1732 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#23780625, C2×#23780626, C2×#23780624, … |
| maximal normal subgroup of | C2×#23780625, C2×#23780626, C2×#23780624, … |
| maximal quotient of | D3×D1729, C2×C3×D1729, C2×D5187, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6916, 21);