Finite Group DatabasebetaFinite Group Databasebeta| order | 37076 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D299⋊D31 |
| unambiguous semidirect product | D403⋊D23 |
| unambiguous semidirect product | D713⋊D13 |
| Fitting, socle, derived, Hall | C13×C23×C31 ⋊ C22 |
| Hall | C23×C31 ⋊ C2×D13 |
| Hall | C13×C31 ⋊ C2×D23 |
| Hall | C13×C23 ⋊ C2×D31 |
| Sylow | C31 ⋊ D13×D23 |
| Sylow | C23 ⋊ D13×D31 |
| Sylow | C13 ⋊ D23×D31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C23×C31 | C22 |
| LCS | G ▷ C13×C23×C31 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9269 |
Polycyclic presentation:
2^2,13,23,31|d^a=d^22,e^a=e^30,c^b=c^12,d^b=d^222369 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37076, 20);