Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#14268437 |
| Fitting, socle | C2×C32×C52 ⋊ C2×C4 |
| derived, Hall | C32×C52 ⋊ C22×C4 |
| Sylow | C52 ⋊ C2×D3×Dic3 |
| Sylow | C32 ⋊ C2×D5⋊AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #14268437 |
| commutator, hypocenter | C32×C52 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C52 | C2×C4 |
| prime radical | C2×C3×D15⋊D5 | C2 |
| cosocle | C32×C5⋊D5 | C23 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 ◁ C2 | |
538 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 538 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) = 120 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#10597182, C2×D3×D5⋊ΓL(1,𝔽16), C2×#72222577 |
| maximal normal subgroup of | C2×D3×#10597182, C2×D3×D5⋊ΓL(1,𝔽16), C2×#72222577 |
Past the SmallGroups library coverage — no SmallGroups id.