Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D5⋊ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D5⋊(C3⋊#170) |
| derived, Hall | C3×C52 ⋊ C2×C8 |
| Sylow | C52 ⋊ C2×C3⋊C8 |
| Sylow | C3 ⋊ D5⋊#170 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5⋊ΓL(1,𝔽16) |
| commutator, hypocenter | C3×C52 | C2×C8 |
| Fitting, socle | C2×C3×C52 | C2×C4 |
| prime radical | C2×C3×C5×D5 | C4 |
| cosocle | C3×#1039 | C22 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^4,3,5^2|a^2=c,b^2=d,c^2=d,e^a=e^2,f^a=f^2,g^a=g^2,f^b=f^4,f^c=f^4,g^c=g^460 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 562);