Finite Group DatabasebetaFinite Group Databasebeta| order | 17427 |
| isoclinism | isoclinic class of C157⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×C157⋊C3 |
| unambiguous semidirect product | C157⋊(C3×C37) |
| Fitting, socle, Hall | C37×C157 ⋊ C3 |
| derived, Sylow | C157 ⋊ C3×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | C157⋊C3 |
| commutator, cosocle, hypocenter | C157 | C3×C37 |
| Frattini | C1 | G |
| Fitting, socle | C37×C157 | C3 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C37 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5809 |
2035 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C37×C157⋊C3, C37×D157⋊C3, D37×C157⋊C3, … |
| maximal normal subgroup of | C2×C37×C157⋊C3, C37×D157⋊C3, D37×C157⋊C3, … |
| maximal quotient of | C2×C37×C157⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17427, 2);