Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C5 |
| direct product | D32×#1044 |
| Fitting, socle, derived, Hall | C32×C52 ⋊ C22×C4 |
| Sylow | C52 ⋊ C4×D32 |
| Sylow | C32 ⋊ C22×#1044 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C52 | C22×C4 |
| prime radical | D32×C5⋊D5 | C2 |
| cosocle | C32×C5⋊D5 | C23 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 | |
602 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 602 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.
90 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#14268436, D32×D5⋊AGL(1,𝔽5), D3×C3⋊D3×#1044, … |
| maximal normal subgroup of | D32×D5⋊AGL(1,𝔽5), C2×D32×#1044 |
| maximal quotient of | D3×#14268436, D3×C3⋊D3×#1044, C2×D32×#1044 |
Past the SmallGroups library coverage — no SmallGroups id.