Finite Group DatabasebetaFinite Group Databasebeta| order | 7100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | AGL(1,𝔽5)×C71⋊C5 |
| unambiguous semidirect product | (AGL(1,𝔽5)×C71)⋊C5 |
| Fitting, socle, derived | C5×C71 ⋊ C4×C5 |
| Hall | C5×C71⋊C5 ⋊ C4 |
| Sylow | C71 ⋊ C5×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C71 | C4×C5 |
| LCS | G ▷ C5×C71 | |
| UCS | C1 | |
26 conjugacy classes of subgroups.
95 conjugacy classes — view the full character table.
| maximal subgroup of | C3×AGL(1,𝔽5)×C71⋊C5, ΓL(1,𝔽16)×C71⋊C5 |
| maximal normal subgroup of | C3×AGL(1,𝔽5)×C71⋊C5 |
| maximal quotient of | C3×AGL(1,𝔽5)×C71⋊C5, ΓL(1,𝔽16)×C71⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7100, 28);