Finite Group DatabasebetaFinite Group Databasebeta| order | 31164 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C49⋊#6157) |
| unambiguous semidirect product | C49⋊(C3⋊#6157) |
| Fitting, derived, Hall | C3×C49×C53 ⋊ C4 |
| Hall | C49×C53 ⋊ Dic3 |
| Hall | C3×C53 ⋊ Dic49 |
| Hall | C3×C49 ⋊ #6157 |
| Sylow | C53 ⋊ Dic147 |
| Sylow | C49 ⋊ C3⋊#6157 |
| Sylow | C3 ⋊ C49⋊#6157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C3×C49×C53 | C4 |
| Frattini | C7 | C3⋊(C7⋊#6157) |
| socle | C3×C7×C53 | Dic7 |
| prime radical | C3×C7×D53 | D7 |
| cosocle | C3×C49×D53 | C2 |
| LCS | G ▷ C3×C49×C53 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7791 |
Polycyclic presentation:
2^2,3,7,53,7|a^2=b,d^7=f^6,c^a=c^2,d^a=d^6f,e^a=e^30,f^a=f^6,e^b=e^522061 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31164, 25);