Finite Group DatabasebetaFinite Group Databasebeta| order | 1904 |
| isoclinism | isoclinic class of #3633 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×#3633 |
| Fitting, socle | C2×C7×C17 ⋊ C8 |
| derived, Sylow | C17 ⋊ C2×C7×C8 |
| Hall | C7×C17 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | #3633 |
| commutator, hypocenter | C17 | C2×C7×C8 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C17 | C8 |
| prime radical | C2×C7×D17 | C4 |
| cosocle | #595 | C22×C7 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C7 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 238 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C7×AGL(1,𝔽17), C2×D7×#3633, C2×C7⋊AGL(1,𝔽17), … |
| maximal normal subgroup of | C2×C7×AGL(1,𝔽17), C2×D7×#3633, C2×C7⋊AGL(1,𝔽17), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1904, 176);