Finite Group DatabasebetaFinite Group Databasebeta| order | 11618 |
| isoclinism | isoclinic class of D37 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C157 · Schur multiplier (H2) = C1 |
| direct product | D37×C157 |
| unambiguous semidirect product | C37⋊(C2×C157) |
| Fitting, socle, Hall | C37×C157 ⋊ C2 |
| derived, Sylow | C37 ⋊ C2×C157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C157 | D37 |
| commutator, cosocle, hypocenter | C37 | C2×C157 |
| Frattini | C1 | G |
| Fitting, socle | C37×C157 | C2 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C157 | |
8 conjugacy classes of subgroups.
3140 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #3866×C157, #37551217, D37×D157, … |
| maximal normal subgroup of | #3866×C157, #37551217, D37×D157, … |
| maximal quotient of | Dic37×C157, C2×D37×C157, C3×D37×C157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11618, 1);