Finite Group DatabasebetaFinite Group Databasebeta| order | 32116 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(C31⋊#3866) |
| unambiguous semidirect product | C31⋊(C7⋊#3866) |
| Fitting, socle, derived, Hall | C7×C31×C37 ⋊ C4 |
| Hall | C31×C37 ⋊ Dic7 |
| Hall | C7×C37 ⋊ Dic31 |
| Hall | C7×C31 ⋊ #3866 |
| Sylow | C37 ⋊ Dic217 |
| Sylow | C31 ⋊ C7⋊#3866 |
| Sylow | C7 ⋊ C31⋊#3866 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C31×C37 | C4 |
| prime radical, cosocle | C7×C31×D37 | C2 |
| LCS | G ▷ C7×C31×C37 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8029 |
Polycyclic presentation:
2^2,7,31,37|a^2=b,c^a=c^6,d^a=d^30,e^a=e^31,e^b=e^362173 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32116, 15);