Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of C3⋊#1043 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×C3⋊#1043 |
| Fitting, socle | C22×C3×C52 ⋊ C4 |
| derived, Hall | C3×C52 ⋊ C22×C4 |
| Sylow | C52 ⋊ C22×Dic3 |
| Sylow | C3 ⋊ C22×#1043 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊#1043 |
| commutator, hypocenter | C3×C52 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C52 | C4 |
| prime radical | C22×C3×C5⋊D5 | C2 |
| cosocle | C3×C5⋊D5 | C23 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C22 | |
432 conjugacy classes of subgroups.
| transitive degree | μt(G) = 300 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D3×#1043, #72224574, #72224581, … |
| maximal normal subgroup of | C22×D3×#1043, #72224574, #72224581, … |
| maximal quotient of | C22×C3⋊(C3⋊#1043), C2×C4×C3⋊#1043, C2×C4⋊(C3⋊#1043), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 1022);