Finite Group DatabasebetaFinite Group Databasebeta| order | 2720 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#13062854 |
| Fitting, socle | C2×C5×C17 ⋊ C16 |
| derived, Hall | C5×C17 ⋊ C2×C16 |
| Sylow | C17 ⋊ C2×#674 |
| Sylow | C5 ⋊ C2×AGL(1,𝔽17) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #13062854 |
| commutator, hypocenter | C5×C17 | C2×C16 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C17 | C16 |
| prime radical | C2×C5×D17 | C8 |
| cosocle | #10621779 | C22 |
| LCS | G ▷ C5×C17 | |
| UCS | C1 ◁ C2 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 170 |
50 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72222280, #72244822 |
| maximal normal subgroup of | C2×#72222280 |
| maximal quotient of | #72244822 |
Past the SmallGroups library coverage — no SmallGroups id.