Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D3×#6057 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C5 |
| direct product | D3×#6057 |
| Fitting, socle, Hall | C3×C52 ⋊ C2×Q8 |
| Sylow | C52 ⋊ D3×Q8 |
| Sylow | C3 ⋊ C2×#6057 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle | C3×C5⋊D5 | C23 |
| Fitting, socle, hypocenter | C3×C52 | C2×Q8 |
| prime radical | D3×C5⋊D5 | C22 |
| LCS | G ▷ C3×C5⋊D5 ▷ C3×C52 | |
| UCS | C1 | |
124 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30 |
24 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 962);