Finite Group DatabasebetaFinite Group Databasebeta| order | 7680 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C24 |
| direct product | D5×#11714270 |
| derived | C5×#5464 ⋊ C2×C4 |
| Sylow | C5 ⋊ C2×#11714270 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | C5×#5464 | C2×C4 |
| Frattini | C23 | D5×#1020 |
| Fitting | C5×#3532 | C2×D3 |
| socle | C22×C5 | C2×#5936 |
| prime radical | D5×#3532⋊C3 | C2 |
| cosocle | C5×#3532⋊C3 | C22 |
| LCS | G ▷ C5×#5464 | |
| UCS | C1 | |
3142 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 3142 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
96 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#11714270, D5×AGL(2,ℤ/4), #72243780 |
| maximal normal subgroup of | AGL(1,𝔽5)×#11714270, D5×AGL(2,ℤ/4), #72243780 |
Past the SmallGroups library coverage — no SmallGroups id.