Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D3×D5×ΓL(1,𝔽16) |
| Fitting, socle, derived, Hall | C32×C52 ⋊ C22×C4 |
| Sylow | C52 ⋊ C2×D3×Dic3 |
| Sylow | C32 ⋊ C2×D5×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C52 | C22×C4 |
| prime radical | C3×D3×D52 | C2 |
| cosocle | C32×C5×D5 | C23 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 | |
486 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | D3×ΓL(1,𝔽16)⋊AGL(1,𝔽5), D32×D5×AGL(1,𝔽5), D3×AGL(1,𝔽5)×ΓL(1,𝔽16) |
| maximal normal subgroup of | D3×ΓL(1,𝔽16)⋊AGL(1,𝔽5), D32×D5×AGL(1,𝔽5), D3×AGL(1,𝔽5)×ΓL(1,𝔽16) |
Past the SmallGroups library coverage — no SmallGroups id.