Finite Group DatabasebetaFinite Group Databasebeta| order | 2720 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×AGL(1,𝔽17) |
| Fitting, socle | C2×C5×C17 ⋊ C16 |
| derived, Sylow | C17 ⋊ C2×C5×C16 |
| Hall | C5×C17 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | AGL(1,𝔽17) |
| commutator, hypocenter | C17 | C2×C5×C16 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C17 | C16 |
| prime radical | C2×C5×D17 | C8 |
| cosocle | #3633 | C22×C5 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C5 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 170 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D5×AGL(1,𝔽17), C5×D5×AGL(1,𝔽17), AGL(1,𝔽11)×AGL(1,𝔽17) |
| maximal normal subgroup of | C2×D5×AGL(1,𝔽17) |
| maximal quotient of | C5×D5×AGL(1,𝔽17), AGL(1,𝔽11)×AGL(1,𝔽17) |
Past the SmallGroups library coverage — no SmallGroups id.