Finite Group DatabasebetaFinite Group Databasebeta| order | 1160 |
| isoclinism | isoclinic class of D5⋊#1181 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D5⋊#1181 |
| unambiguous semidirect product | D29⋊AGL(1,𝔽5) |
| unambiguous semidirect product | #10596814⋊C2 |
| unambiguous semidirect product | #10596815⋊C2 |
| Fitting, socle, derived, Hall | C5×C29 ⋊ C2×C4 |
| Sylow | C29 ⋊ C2×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×#1181 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C29 | C2×C4 |
| prime radical | D5×D29 | C2 |
| cosocle | D145 | C22 |
| LCS | G ▷ C5×C29 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 34 |
| transitive degree | μt(G) = 145 |
Polycyclic presentation:
2^3,5,29|a^2=c,d^a=d^2,e^a=e^12,d^b=d^4,d^c=d^4,e^c=e^2838 conjugacy classes — view the full character table.
| maximal subgroup of | #72218696, AGL(1,𝔽5)×#1181, C2×D5⋊#1181 |
| maximal normal subgroup of | #72218696, AGL(1,𝔽5)×#1181, C2×D5⋊#1181 |
| maximal quotient of | C2×D5⋊#1181 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1160, 36);