Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #1042 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×C3×#1042 |
| unambiguous semidirect product | D5⋊(C2×C3×Dic5) |
| Fitting, socle | C22×C3×C52 ⋊ C4 |
| derived, Sylow | C52 ⋊ C22×C3×C4 |
| Hall | C3×C52 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #1042 |
| commutator, hypocenter | C52 | C22×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C52 | C4 |
| prime radical | C22×C3×C5×D5 | C2 |
| cosocle | C5×D5 | C23×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22×C3 | |
226 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×C4×#1042 |
| maximal normal subgroup of | C2×C3×C4×#1042 |
| maximal quotient of | C2×C3×C4×#1042 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 1020);