Finite Group DatabasebetaFinite Group Databasebeta| order | 2240 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | D5×#6500 |
| Fitting | C2×C5×C7×D4 ⋊ C22 |
| Hall | C5×C7 ⋊ C2×#120 |
| Sylow | C7 ⋊ D5×#120 |
| Sylow | C5 ⋊ C2×#6500 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D5×D7 |
| commutator, socle, cosocle | C22×C5×C7 | C24 |
| Fitting | C2×C5×C7×D4 | C22 |
| hypercenter | C2×D4 | D5×D7 |
| hypocenter | C5×C7 | C2×#120 |
| LCS | G ▷ C22×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
1324 conjugacy classes of subgroups.
176 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#6500⋊C3, D5×D7×#120, AGL(1,𝔽5)×#6500, … |
| maximal normal subgroup of | D5×#6500⋊C3, D5×D7×#120, AGL(1,𝔽5)×#6500, … |
Past the SmallGroups library coverage — no SmallGroups id.