Finite Group DatabasebetaFinite Group Databasebeta| order | 32116 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D217⋊D37 |
| unambiguous semidirect product | D259⋊D31 |
| unambiguous semidirect product | D1147⋊D7 |
| Fitting, socle, derived, Hall | C7×C31×C37 ⋊ C22 |
| Hall | C31×C37 ⋊ C2×D7 |
| Hall | C7×C37 ⋊ C2×D31 |
| Hall | C7×C31 ⋊ C2×D37 |
| Sylow | C37 ⋊ D7×D31 |
| Sylow | C31 ⋊ D7×D37 |
| Sylow | C7 ⋊ D31×D37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C31×C37 | C22 |
| LCS | G ▷ C7×C31×C37 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8029 |
Polycyclic presentation:
2^2,7,31,37|d^a=d^30,e^a=e^36,c^b=c^6,d^b=d^302065 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32116, 20);