Finite Group DatabasebetaFinite Group Databasebeta| order | 7820 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17×C23 · Schur multiplier (H2) = C1 |
| direct product | C17×AGL(1,𝔽5)×C23 |
| Fitting, socle, Hall | C5×C17×C23 ⋊ C4 |
| derived, Sylow | C5 ⋊ C4×C17×C23 |
| Hall | C5×C23 ⋊ C4×C17 |
| Hall | C5×C17 ⋊ C4×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17×C23 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C4×C17×C23 |
| Frattini | C1 | G |
| Fitting, socle | C5×C17×C23 | C4 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C17×C23 | |
24 conjugacy classes of subgroups.
1955 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C17×AGL(1,𝔽5)×C23, C17×C23×ΓL(1,𝔽16) |
| maximal normal subgroup of | C3×C17×AGL(1,𝔽5)×C23 |
| maximal quotient of | C3×C17×AGL(1,𝔽5)×C23, C17×C23×ΓL(1,𝔽16) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7820, 13);