Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of C3⋊#1044 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4×C5 |
| direct product | C4×C3⋊#1044 |
| Fitting | C3×C4×C52 ⋊ C4 |
| derived, Hall | C3×C52 ⋊ C42 |
| Sylow | C52 ⋊ C4×Dic3 |
| Sylow | C3 ⋊ C4×#1044 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C3⋊#1044 |
| commutator, hypocenter | C3×C52 | C42 |
| Frattini | C2 | C2×C3⋊#1044 |
| Fitting | C3×C4×C52 | C4 |
| socle | C2×C3×C52 | C2×C4 |
| prime radical, cosocle | C2×C3×C5⋊D5 | C22 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C4 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | #72229444, C4×#10597182, #72230585, … |
| maximal normal subgroup of | #72229444, C4×#10597182, #72230585, … |
| maximal quotient of | C3×C4×C3⋊#1044, Dic3×C3⋊#1044, #72260004, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 746);