Finite Group DatabasebetaFinite Group Databasebeta| order | 7100 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C71 · Schur multiplier (H2) = C1 |
| direct product | C5×AGL(1,𝔽5)×C71 |
| Fitting, socle, Hall | C52×C71 ⋊ C4 |
| derived | C5 ⋊ C4×C5×C71 |
| Sylow | C52 ⋊ C4×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C71 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C4×C5×C71 |
| Frattini | C1 | G |
| Fitting, socle | C52×C71 | C4 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C5×C71 | |
26 conjugacy classes of subgroups.
1775 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×AGL(1,𝔽5)×C71, C5×ΓL(1,𝔽16)×C71 |
| maximal normal subgroup of | C3×C5×AGL(1,𝔽5)×C71 |
| maximal quotient of | C3×C5×AGL(1,𝔽5)×C71, C5×ΓL(1,𝔽16)×C71 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7100, 34);