Finite Group DatabasebetaFinite Group Databasebeta| order | 6800 |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C16 · Schur multiplier (H2) = C5 |
| direct product | C52×AGL(1,𝔽17) |
| Fitting, socle, Hall | C52×C17 ⋊ C16 |
| derived, Sylow | C17 ⋊ C52×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | AGL(1,𝔽17) |
| commutator, hypocenter | C17 | C52×C16 |
| Frattini | C1 | G |
| Fitting, socle | C52×C17 | C16 |
| prime radical | C52×D17 | C8 |
| cosocle | #3633 | C2×C52 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C52 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 425 |
425 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5⋊D5×AGL(1,𝔽17), C5×D5×AGL(1,𝔽17) |
| maximal normal subgroup of | C5⋊D5×AGL(1,𝔽17), C5×D5×AGL(1,𝔽17) |
Past the SmallGroups library coverage — no SmallGroups id.