Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D52 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×C4×D52 |
| Fitting | C3×C4×C52 ⋊ C22 |
| derived, Sylow | C52 ⋊ C22×C3×C4 |
| Hall | C3×C52 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | D52 |
| commutator, hypocenter | C52 | C22×C3×C4 |
| Frattini | C2 | C2×C3×D52 |
| Fitting | C3×C4×C52 | C22 |
| socle | C2×C3×C52 | C23 |
| prime radical | C2×C3×D52 | C2 |
| cosocle | C2×C52 | C23×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C3×C4 | |
248 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 248 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 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#6732, C2×C3×C4×D52, C3×#11717471, … |
| maximal normal subgroup of | C2×C3×C4×D52, C3×#11717471, C3×C4×D5⋊AGL(1,𝔽5), … |
| maximal quotient of | C2×C3×C4×D52, C3×C4×D15⋊D5, C3×D52×Dic3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 764);