Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| isoclinism | isoclinic class of D5⋊#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C3×D5⋊#157 |
| Fitting, socle | C2×C33×C5 ⋊ C2×C4 |
| derived | C32×C5 ⋊ C22×C3×C4 |
| Hall | C33×C5 ⋊ C22×C4 |
| Sylow | C33 ⋊ C22×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C22×C3×#157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D5⋊#157 |
| commutator, hypocenter | C32×C5 | C22×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C33×C5 | C2×C4 |
| prime radical | C2×C3×D5×C3⋊D3 | C2 |
| cosocle | C3⋊D15 | C23×C3 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C2×C3 | |
384 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
108 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×AGL(1,𝔽5)×#157, AGL(1,𝔽7)×D5⋊#157, C2×C3×#10624307, … |
| maximal normal subgroup of | C2×C3×AGL(1,𝔽5)×#157, C2×C3×#10624307, C2×C3×D32⋊AGL(1,𝔽5) |
| maximal quotient of | AGL(1,𝔽7)×D5⋊#157 |
Past the SmallGroups library coverage — no SmallGroups id.