Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D5×ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×D5×ΓL(1,𝔽16) |
| unambiguous semidirect product | D5⋊(D5×Dic3) |
| Fitting, socle | C2×C3×C52 ⋊ C2×C4 |
| derived, Hall | C3×C52 ⋊ C22×C4 |
| Sylow | C52 ⋊ C22×Dic3 |
| Sylow | C3 ⋊ C2×D5×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5×ΓL(1,𝔽16) |
| commutator, hypocenter | C3×C52 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C52 | C2×C4 |
| prime radical | C2×C3×D52 | C2 |
| cosocle | C3×C5×D5 | C23 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
226 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 998);