Finite Group DatabasebetaFinite Group Databasebeta| order | 8092 |
| isoclinism | isoclinic class of D119 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C17 · Schur multiplier (H2) = C2 |
| direct product | C2×C17×D119 |
| unambiguous semidirect product | (C2×C7)⋊(C17×D17) |
| unambiguous semidirect product | (C2×C17)⋊(D7×C17) |
| Fitting, socle | C2×C7×C172 ⋊ C2 |
| derived | C7×C17 ⋊ C22×C17 |
| Hall | C7×C172 ⋊ C22 |
| Sylow | C172 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×C17×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17 | D119 |
| commutator, hypocenter | C7×C17 | C22×C17 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C172 | C2 |
| LCS | G ▷ C7×C17 | |
| UCS | C1 ◁ C2×C17 | |
72 conjugacy classes of subgroups.
2074 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C17×C17⋊AGL(1,𝔽7), C2×C7⋊#13181892, D3×C17×D119, … |
| maximal normal subgroup of | C2×C17×C17⋊AGL(1,𝔽7), C2×C3×C17×D119 |
| maximal quotient of | D3×C17×D119, C2×C3×C17×D119, C2×C17×D357 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8092, 33);