Finite Group DatabasebetaFinite Group Databasebeta| order | 3360 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | AGL(1,𝔽7)×#711 |
| Fitting | C5×C7×D4 ⋊ C22×C3 |
| Hall | D7×#711 ⋊ C3 |
| Hall | C5×ΓL(1,𝔽8) ⋊ C2×#41 |
| Hall | C5×C7 ⋊ C2×C3×#41 |
| Hall | ΓL(1,𝔽8) ⋊ C2×#711 |
| Sylow | C7 ⋊ C2×C3×#711 |
| Sylow | C5 ⋊ #41×AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D5×AGL(1,𝔽7) |
| commutator, socle, cosocle | C2×C5×C7 | C24×C3 |
| Fitting | C5×C7×D4 | C22×C3 |
| hypercenter | D4 | D5×AGL(1,𝔽7) |
| hypocenter | C5×C7 | C2×C3×#41 |
| LCS | G ▷ C2×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C2 ◁ D4 | |
656 conjugacy classes of subgroups.
140 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#41×AGL(1,𝔽7), AGL(1,𝔽7)×#4057 |
| maximal normal subgroup of | D5×#41×AGL(1,𝔽7), AGL(1,𝔽7)×#4057 |
Past the SmallGroups library coverage — no SmallGroups id.