Finite Group DatabasebetaFinite Group Databasebeta| order | 5712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×#72229434 |
| Fitting, socle | C2×C7×C17 ⋊ C3×C8 |
| derived, Hall | C7×C17 ⋊ C2×C3×C8 |
| Hall | C2×C7⋊#3633 ⋊ C3 |
| Hall | C17×ΓL(1,𝔽8) ⋊ C2×C8 |
| Hall | ΓL(1,𝔽8) ⋊ C2×#3633 |
| Sylow | C17 ⋊ C2×ΓL(1,𝔽8)⋊C8 |
| Sylow | C7 ⋊ C2×C3×#3633 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72229434 |
| commutator, hypocenter | C7×C17 | C2×C3×C8 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C17 | C3×C8 |
| prime radical | C2×ΓL(1,𝔽8)×D17 | C4 |
| cosocle | C7×#595 | C22×C3 |
| LCS | G ▷ C7×C17 | |
| UCS | C1 ◁ C2 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 238 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽7)×#3633 |
| maximal normal subgroup of | C2×AGL(1,𝔽7)×#3633 |
Past the SmallGroups library coverage — no SmallGroups id.