Finite Group DatabasebetaFinite Group Databasebeta| order | 1160 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C29 · Schur multiplier (H2) = C2 |
| direct product | C2×AGL(1,𝔽5)×C29 |
| unambiguous semidirect product | D5⋊(C4×C29) |
| Fitting, socle | C2×C5×C29 ⋊ C4 |
| derived, Sylow | C5 ⋊ C2×C4×C29 |
| Hall | C5×C29 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C29 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C2×C4×C29 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C29 | C4 |
| prime radical | C2×D5×C29 | C2 |
| cosocle | D5 | C22×C29 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C29 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 290 |
290 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×AGL(1,𝔽5)×C29⋊C7, C2×AGL(1,𝔽5)×D29, C22×AGL(1,𝔽5)×C29 |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×C29⋊C7, C2×AGL(1,𝔽5)×D29, C22×AGL(1,𝔽5)×C29 |
| maximal quotient of | C22×AGL(1,𝔽5)×C29 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1160, 40);