Finite Group DatabasebetaFinite Group Databasebeta| order | 1360 |
| isoclinism | isoclinic class of AGL(1,𝔽5)×D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×AGL(1,𝔽5)×D17 |
| unambiguous semidirect product | D5⋊(C4×D17) |
| unambiguous semidirect product | (C17×AGL(1,𝔽5))⋊C22 |
| unambiguous semidirect product | #66774⋊C22 |
| Fitting, socle | C2×C5×C17 ⋊ C2×C4 |
| derived, Hall | C5×C17 ⋊ C22×C4 |
| Sylow | C17 ⋊ C22×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×C4×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | AGL(1,𝔽5)×D17 |
| commutator, hypocenter | C5×C17 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C17 | C2×C4 |
| prime radical | C2×D5×D17 | C2 |
| cosocle | D5×C17 | C23 |
| LCS | G ▷ C5×C17 | |
| UCS | C1 ◁ C2 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 170 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽5)×#595, D17×D5⋊AGL(1,𝔽5) |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×#595 |
| maximal quotient of | D17×D5⋊AGL(1,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1360, 232);