Finite Group DatabasebetaFinite Group Databasebeta| order | 10180 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C509 · Schur multiplier (H2) = C1 |
| direct product | AGL(1,𝔽5)×C509 |
| Fitting, socle, Hall | C5×C509 ⋊ C4 |
| derived, Sylow | C5 ⋊ C4×C509 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C509 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C4×C509 |
| Frattini | C1 | G |
| Fitting, socle | C5×C509 | C4 |
| prime radical | D5×C509 | C2 |
| cosocle | D5 | C2×C509 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C509 | |
12 conjugacy classes of subgroups.
2545 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×AGL(1,𝔽5)×C509, ΓL(1,𝔽16)×C509 |
| maximal normal subgroup of | C3×AGL(1,𝔽5)×C509 |
| maximal quotient of | C3×AGL(1,𝔽5)×C509, ΓL(1,𝔽16)×C509 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10180, 7);