Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #1044 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C5 |
| direct product | C22×C3×#1044 |
| Fitting, socle | C22×C3×C52 ⋊ C4 |
| derived, Sylow | C52 ⋊ C22×C3×C4 |
| Hall | C3×C52 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #1044 |
| 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 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 1019);