Finite Group DatabasebetaFinite Group Databasebeta| order | 2520 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | D5×A4×ΓL(1,𝔽8) |
| Fitting, socle, derived | C22×C5×C7 ⋊ C2×C32 |
| Hall | C22×C7×D5 ⋊ C32 |
| Hall | C22×D5 ⋊ C3×ΓL(1,𝔽8) |
| Hall | C5×C7 ⋊ C2×C3×A4 |
| Sylow | C7 ⋊ C3×D5×A4 |
| Sylow | C5 ⋊ C2×A4×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C5×C7 | C2×C32 |
| LCS | G ▷ C22×C5×C7 | |
| UCS | C1 | |
128 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
80 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.