Finite Group DatabasebetaFinite Group Databasebeta| order | 5516 |
| isoclinism | isoclinic class of D197 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×D197 |
| Fitting, socle | C2×C7×C197 ⋊ C2 |
| derived, Sylow | C197 ⋊ C22×C7 |
| Hall | C7×C197 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D197 |
| commutator, hypocenter | C197 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C197 | C2 |
| LCS | G ▷ C197 | |
| UCS | C1 ◁ C2×C7 | |
20 conjugacy classes of subgroups.
1400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×ΓL(1,𝔽8)×D197, D3×C7×D197, C2×C7×D591, … |
| maximal normal subgroup of | C2×ΓL(1,𝔽8)×D197, C2×C3×C7×D197, C2×C5×C7×D197, … |
| maximal quotient of | D3×C7×D197, C2×C7×D591, C2×C3×C7×D197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5516, 16);