Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C3×C4 |
| direct product | AGL(1,𝔽5)×C3⋊ΓL(1,𝔽16) |
| Fitting, socle, derived, Hall | C32×C52 ⋊ C42 |
| Sylow | C52 ⋊ C4×C3⋊Dic3 |
| Sylow | C32 ⋊ AGL(1,𝔽5)2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C52 | C42 |
| prime radical, cosocle | C32×D52 | C22 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 | |
378 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×AGL(1,𝔽5)2, D3×AGL(1,𝔽5)×ΓL(1,𝔽16) |
| maximal normal subgroup of | C3⋊D3×AGL(1,𝔽5)2, D3×AGL(1,𝔽5)×ΓL(1,𝔽16) |
Past the SmallGroups library coverage — no SmallGroups id.