Finite Group DatabasebetaFinite Group Databasebeta| order | 3780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×D15×AGL(1,𝔽7) |
| Fitting, socle | C32×C5×C7 ⋊ C22×C3 |
| derived | C3×C5×C7 ⋊ C22×C32 |
| Hall | C32×C5×ΓL(1,𝔽8) ⋊ C22 |
| Hall | C32×ΓL(1,𝔽8) ⋊ C2×D5 |
| Hall | C5×C7 ⋊ C2×C32×D3 |
| Sylow | C7 ⋊ C2×C32×D15 |
| Sylow | C5 ⋊ C3×D3×AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D15×AGL(1,𝔽7) |
| commutator, cosocle, hypocenter | C3×C5×C7 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C7 | C22×C3 |
| LCS | G ▷ C3×C5×C7 | |
| UCS | C1 ◁ C3 | |
304 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
189 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×D5×AGL(1,𝔽7), D3×D15×AGL(1,𝔽7), AGL(1,𝔽7)×(C3⋊D3)⋊D5 |
| maximal normal subgroup of | C3×D3×D5×AGL(1,𝔽7), D3×D15×AGL(1,𝔽7), AGL(1,𝔽7)×(C3⋊D3)⋊D5 |
Past the SmallGroups library coverage — no SmallGroups id.