Finite Group DatabasebetaFinite Group Databasebeta| order | 2520 |
| isoclinism | isoclinic class of A4⋊AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×A4⋊AGL(1,𝔽7) |
| Fitting, socle | C22×C5×C7 ⋊ C3×D3 |
| derived | C7×A4 ⋊ C2×C3×C5 |
| Hall | C5×C7 ⋊ C3×S4 |
| Sylow | C7 ⋊ C3×C5×S4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | A4⋊AGL(1,𝔽7) |
| commutator, cosocle, hypocenter | C7×A4 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C7 | C3×D3 |
| LCS | G ▷ C7×A4 | |
| UCS | C1 ◁ C5 | |
96 conjugacy classes of subgroups.
95 conjugacy classes — view the full character table.
| maximal subgroup of | D5×A4⋊AGL(1,𝔽7), C5×S4×AGL(1,𝔽7), #72218805 |
| maximal normal subgroup of | D5×A4⋊AGL(1,𝔽7), C5×S4×AGL(1,𝔽7), #72218805 |
| maximal quotient of | C5×ΓL(1,𝔽8)⋊GL(2,𝔽3) |
Past the SmallGroups library coverage — no SmallGroups id.