Finite Group DatabasebetaFinite Group Databasebeta| order | 7200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C3 |
| direct product | C22×D5⋊(C3⋊ΓL(1,𝔽16)) |
| Fitting, socle | C22×C32×C52 ⋊ C2×C4 |
| derived, Hall | C32×C52 ⋊ C23×C4 |
| Sylow | C52 ⋊ C23×C3⋊Dic3 |
| Sylow | C32 ⋊ C22×D5⋊AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D5⋊(C3⋊ΓL(1,𝔽16)) |
| commutator, hypocenter | C32×C52 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C32×C52 | C2×C4 |
| prime radical | C22×C32×D52 | C2 |
| cosocle | C32×C5⋊D5 | C24 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 ◁ C22 | |
3156 conjugacy classes of subgroups; only the 675 normal subgroups are shown.
This group has 3156 conjugacy classes of subgroups — too many to draw. Only its 675 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 360 |
312 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C3⋊D3×D5⋊AGL(1,𝔽5), C2×#72231471, C2×#72231494 |
| maximal normal subgroup of | C22×C3⋊D3×D5⋊AGL(1,𝔽5), C2×#72231471, C2×#72231494 |
| maximal quotient of | C2×#72231471 |
Past the SmallGroups library coverage — no SmallGroups id.