Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of C52⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C16 · Schur multiplier (H2) = C5 |
| direct product | C16×C52⋊C3 |
| unambiguous semidirect product | (C52×C16)⋊C3 |
| Fitting, Hall | C52×C16 ⋊ C3 |
| derived, Sylow | C52 ⋊ C3×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | C52⋊C3 |
| commutator, hypocenter | C52 | C3×C16 |
| Frattini | C8 | C2×C52⋊C3 |
| Fitting | C52×C16 | C3 |
| socle | C2×C52 | C3×C8 |
| prime radical | C2×C52⋊C3 | C8 |
| cosocle | C52×C8 | C2×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C16 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 185);