Finite Group DatabasebetaFinite Group Databasebeta| order | 31164 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C3⋊(C7⋊Dic371) |
| unambiguous semidirect product | C7⋊Dic1113 |
| derived, Hall | C3×C72×C53 ⋊ C4 |
| Hall | C72×C53 ⋊ Dic3 |
| Hall | C3×C53 ⋊ C7⋊Dic7 |
| Hall | C3×C72 ⋊ Dic53 |
| Sylow | C53 ⋊ C3⋊(C7⋊Dic7) |
| Sylow | C72 ⋊ Dic159 |
| Sylow | C3 ⋊ C7⋊Dic371 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C7⋊D371) |
| commutator, hypocenter | C3×C72×C53 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C72×C53 | C2 |
| LCS | G ▷ C3×C72×C53 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31164 |
Polycyclic presentation:
2,3,7^2,53,2|a^2=f,b^a=b^2,c^a=c^6,d^a=d^6,e^a=e^527794 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31164, 64);