Finite Group DatabasebetaFinite Group Databasebeta| order | 15651 |
| isoclinism | isoclinic class of C37⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C47 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C37×C47 ⋊ C3 |
| derived, Sylow | C37 ⋊ C32×C47 |
| Hall | C37×C47 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C47 | C37⋊C3 |
| commutator, cosocle, hypocenter | C37 | C32×C47 |
| Frattini | C1 | G |
| Fitting, socle | C3×C37×C47 | C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C3×C47 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5217 |
2115 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C47×D37⋊C3, C3×C47⋊(D37⋊C3), C3×D47×C37⋊C3, … |
| maximal normal subgroup of | C3×C47×D37⋊C3, C3×C47⋊(D37⋊C3), C3×D47×C37⋊C3, … |
| maximal quotient of | C2×C3×C47×C37⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15651, 5);