Finite Group DatabasebetaFinite Group Databasebeta| order | 2240 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C24×D5×D7 |
| Fitting, socle | C24×C5×C7 ⋊ C22 |
| derived, Hall | C5×C7 ⋊ C26 |
| Sylow | C7 ⋊ C25×D5 |
| Sylow | C5 ⋊ C25×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D5×D7 |
| commutator, cosocle, hypocenter | C5×C7 | C26 |
| Frattini | C1 | G |
| Fitting, socle | C24×C5×C7 | C22 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C24 | |
11300 conjugacy classes of subgroups; only the 3640 normal subgroups are shown.
This group has 11300 conjugacy classes of subgroups — too many to draw. Only its 3640 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C24×D5×AGL(1,𝔽7), C24×D7×AGL(1,𝔽5), D5×D7×#120, … |
| maximal normal subgroup of | C24×D5×AGL(1,𝔽7), C24×D7×AGL(1,𝔽5), D5×D7×#120, … |
Past the SmallGroups library coverage — no SmallGroups id.