Finite Group DatabasebetaFinite Group Databasebeta| order | 4716 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C131⋊#157 |
| Fitting, socle, derived, Hall | C32×C131 ⋊ C4 |
| Sylow | C131 ⋊ #157 |
| Sylow | C32 ⋊ Dic131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C131 | C4 |
| prime radical, cosocle | C3⋊D3×C131 | C2 |
| LCS | G ▷ C32×C131 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 786 |
Polycyclic presentation:
2^2,3^2,131|a^2=b,c^a=cd,d^a=cd^2,e^a=e^130,c^b=c^2,d^b=d^2396 conjugacy classes — view the full character table.
| maximal subgroup of | (C131⋊C5)⋊#157, C5×C131⋊#157, C131⋊#4380, … |
| maximal normal subgroup of | (C131⋊C5)⋊#157, C5×C131⋊#157, C7×C131⋊#157 |
| maximal quotient of | C5×C131⋊#157, C131⋊#4380, C131⋊#4379, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4716, 24);