Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D3×#1044 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4×C5 |
| direct product | Dic3×#1044 |
| derived, Hall | C3×C52 ⋊ C42 |
| Sylow | C52 ⋊ C4×Dic3 |
| Sylow | C3 ⋊ C4×#1044 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×#1044 |
| commutator, hypocenter | C3×C52 | C42 |
| Fitting, socle | C2×C3×C52 | C2×C4 |
| prime radical, cosocle | C2×C3×C5⋊D5 | C22 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | #72230575, #72230576, #72230579, … |
| maximal normal subgroup of | #72230575, #72230576, #72230579, … |
| maximal quotient of | #72230605, C3×Dic3×#1044, Dic3×C3⋊#1044, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 552);