Finite Group DatabasebetaFinite Group Databasebeta| order | 16761 |
| isoclinism | isoclinic class of C37⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C151 · Schur multiplier (H2) = C1 |
| direct product | C37⋊C3×C151 |
| unambiguous semidirect product | C37⋊(C3×C151) |
| Fitting, socle, Hall | C37×C151 ⋊ C3 |
| derived, Sylow | C37 ⋊ C3×C151 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C151 | C37⋊C3 |
| commutator, cosocle, hypocenter | C37 | C3×C151 |
| Frattini | C1 | G |
| Fitting, socle | C37×C151 | C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C151 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5587 |
2265 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C37⋊C3×C151, C37⋊C3×D151, C151×D37⋊C3, … |
| maximal normal subgroup of | C2×C37⋊C3×C151, C37⋊C3×D151, C151×D37⋊C3, … |
| maximal quotient of | C2×C37⋊C3×C151 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16761, 1);