Finite Group DatabasebetaFinite Group Databasebeta| order | 1904 |
| isoclinism | isoclinic class of D7×#3633 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | D7×#3633 |
| unambiguous semidirect product | (C7×#3633)⋊C2 |
| unambiguous semidirect product | (C7⋊#3633)⋊C2 |
| Fitting, socle, derived, Hall | C7×C17 ⋊ C2×C8 |
| Sylow | C17 ⋊ C8×D7 |
| Sylow | C7 ⋊ C2×#3633 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C17 | C2×C8 |
| prime radical | D7×D17 | C4 |
| cosocle | C7×#595 | C22 |
| LCS | G ▷ C7×C17 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 119 |
50 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×#3633, D7×AGL(1,𝔽17), C2×D7×#3633 |
| maximal normal subgroup of | AGL(1,𝔽7)×#3633, D7×AGL(1,𝔽17), C2×D7×#3633 |
| maximal quotient of | C2×D7×#3633 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1904, 174);