Finite Group DatabasebetaFinite Group Databasebeta| order | 1160 |
| isoclinism | isoclinic class of AGL(1,𝔽5)×D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | AGL(1,𝔽5)×D29 |
| unambiguous semidirect product | (AGL(1,𝔽5)×C29)⋊C2 |
| unambiguous semidirect product | #10596816⋊C2 |
| Fitting, socle, derived, Hall | C5×C29 ⋊ C2×C4 |
| Sylow | C29 ⋊ C2×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×D29 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C29 | C2×C4 |
| prime radical | D5×D29 | C2 |
| cosocle | D5×C29 | C22 |
| LCS | G ▷ C5×C29 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 34 |
| transitive degree | μt(G) = 145 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×D29⋊C7, AGL(1,𝔽5)×#1181, C2×AGL(1,𝔽5)×D29 |
| maximal normal subgroup of | AGL(1,𝔽5)×D29⋊C7, AGL(1,𝔽5)×#1181, C2×AGL(1,𝔽5)×D29 |
| maximal quotient of | C2×AGL(1,𝔽5)×D29 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1160, 37);