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 | C2×C3×#6036 |
| derived, Sylow | C52 ⋊ C22×C3×C4 |
| Hall | C3×C52 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | D52 |
| commutator, hypocenter | C52 | C22×C3×C4 |
| Frattini | C2 | C2×C3×D52 |
| Fitting, socle | C22×C3×C52 | C22 |
| prime radical | C22×C3×C5⋊D5 | C2 |
| cosocle | C2×C52 | C23×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22×C3 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×C5⋊#6732, C2×C3×C4×D52, C2×C32×#6036, … |
| maximal normal subgroup of | C2×C3×C4×D52, C2×C32×#6036, C2×C3×#87886, … |
| maximal quotient of | C2×C32×#6036, C3×#11716936, C3×#11717092, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 770);