Finite Group DatabasebetaFinite Group Databasebeta| order | 10508 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C71⋊#3866 |
| Fitting, socle, derived, Hall | C37×C71 ⋊ C4 |
| Sylow | C71 ⋊ #3866 |
| Sylow | C37 ⋊ Dic71 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C37×C71 | C4 |
| prime radical, cosocle | C71×D37 | C2 |
| LCS | G ▷ C37×C71 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,37,71|a^2=b,c^a=c^31,d^a=d^70,c^b=c^36713 conjugacy classes — view the full character table.
| maximal subgroup of | C71⋊(#3866⋊C3), C3×C71⋊#3866, C3⋊(C71⋊#3866) |
| maximal normal subgroup of | C71⋊(#3866⋊C3), C3×C71⋊#3866 |
| maximal quotient of | C3×C71⋊#3866, C3⋊(C71⋊#3866) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10508, 7);