Finite Group DatabasebetaFinite Group Databasebeta| order | 5316 |
| automorphism | Aut(G) order 2349672 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2658 |
| direct product | C2×D1329 |
| unambiguous semidirect product | (C2×C3)⋊D443 |
| unambiguous semidirect product | (C2×C443)⋊D3 |
| Fitting, socle | C2×C3×C443 ⋊ C2 |
| derived, Hall | C3×C443 ⋊ C22 |
| Sylow | C443 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×D443 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1329 |
| commutator, hypocenter | C3×C443 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C443 | C2 |
| LCS | G ▷ C3×C443 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
1332 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D3987, D3×D1329, C2×C3⋊D1329, … |
| maximal normal subgroup of | C2×C3×D1329, C2×C5×D1329, C2×C7×D1329, … |
| maximal quotient of | C2×D3987, D3×D1329, C2×C3⋊D1329, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5316, 8);