Finite Group DatabasebetaFinite Group Databasebeta| order | 1360 |
| isoclinism | isoclinic class of D5⋊#3633 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D5⋊#3633 |
| unambiguous semidirect product | #10621777⋊C2 |
| unambiguous semidirect product | #10621778⋊C2 |
| Fitting, socle, derived, Hall | C5×C17 ⋊ C2×C8 |
| Sylow | C17 ⋊ D5⋊C8 |
| Sylow | C5 ⋊ C2×#3633 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C17 | C2×C8 |
| prime radical | D5×D17 | C4 |
| cosocle | #66772 | C22 |
| LCS | G ▷ C5×C17 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 85 |
Polycyclic presentation:
2^4,5,17|a^2=c,c^2=d,e^a=e^2,f^a=f^9,e^b=e^4,e^c=e^4,f^c=f^13,f^d=f^1628 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#3633, #72244735, C2×D5⋊#3633, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#3633, C2×D5⋊#3633 |
| maximal quotient of | #72244735, C2×D5⋊#3633, #72244782, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1360, 225);