Finite Group DatabasebetaFinite Group Databasebeta| order | 31164 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D21⋊D371 |
| Fitting, socle, derived, Hall | C3×C72×C53 ⋊ C22 |
| Hall | C72×C53 ⋊ C2×D3 |
| Hall | C3×C53 ⋊ D72 |
| Hall | C3×C72 ⋊ C2×D53 |
| Sylow | C53 ⋊ D21⋊D7 |
| Sylow | C72 ⋊ D3×D53 |
| Sylow | C3 ⋊ D7×D371 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C72×C53 | C22 |
| LCS | G ▷ C3×C72×C53 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2226 |
Polycyclic presentation:
2^2,3,7^2,53|d^a=d^6,e^a=e^6,f^a=f^52,c^b=c^2,d^b=d^62235 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31164, 161);