Finite Group DatabasebetaFinite Group Databasebeta| order | 3360 |
| isoclinism | isoclinic class of AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3×C5 · Schur multiplier (H2) = C210 |
| direct product | C24×C5×AGL(1,𝔽7) |
| Fitting, socle | C24×C5×C7 ⋊ C2×C3 |
| derived, Sylow | C7 ⋊ C25×C3×C5 |
| Hall | C24×C5×D7 ⋊ C3 |
| Hall | C24×D7 ⋊ C3×C5 |
| Hall | C5×ΓL(1,𝔽8) ⋊ C25 |
| Hall | C5×C7 ⋊ C25×C3 |
| Hall | ΓL(1,𝔽8) ⋊ C25×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C5 | AGL(1,𝔽7) |
| commutator, cosocle, hypocenter | C7 | C25×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C24×C5×C7 | C2×C3 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C24×C5 | |
2992 conjugacy classes of subgroups.
560 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C24×D5×AGL(1,𝔽7), C5×#120×AGL(1,𝔽7), AGL(1,𝔽7)×#4099 |
| maximal normal subgroup of | C24×D5×AGL(1,𝔽7), C5×#120×AGL(1,𝔽7), AGL(1,𝔽7)×#4099 |
Past the SmallGroups library coverage — no SmallGroups id.