Finite Group DatabasebetaFinite Group Databasebeta| order | 31164 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D147⋊D53 |
| unambiguous semidirect product | D159⋊D49 |
| unambiguous semidirect product | D2597⋊D3 |
| Fitting, derived, Hall | C3×C49×C53 ⋊ C22 |
| Hall | C49×C53 ⋊ C2×D3 |
| Hall | C3×C53 ⋊ C2×D49 |
| Hall | C3×C49 ⋊ C2×D53 |
| Sylow | C53 ⋊ D3×D49 |
| Sylow | C49 ⋊ D3×D53 |
| Sylow | C3 ⋊ D49×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C49×C53 | C22 |
| Frattini | C7 | D21⋊D53 |
| socle | C3×C7×C53 | C2×D7 |
| LCS | G ▷ C3×C49×C53 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7791 |
Polycyclic presentation:
2^2,3,7,53,7|d^7=f^6,d^a=d^6f,e^a=e^52,f^a=f^6,c^b=c^2,d^b=d^6f,f^b=f^62028 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31164, 30);