Finite Group DatabasebetaFinite Group Databasebeta| order | 10508 |
| isoclinism | isoclinic class of #3866 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×#3866 |
| Fitting, socle, Hall | C37×C71 ⋊ C4 |
| derived, Sylow | C37 ⋊ C4×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C71 | #3866 |
| commutator, hypocenter | C37 | C4×C71 |
| Frattini | C1 | G |
| Fitting, socle | C37×C71 | C4 |
| prime radical | C71×D37 | C2 |
| cosocle | D37 | C2×C71 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C71 | |
12 conjugacy classes of subgroups.
923 conjugacy classes — view the full character table.
| maximal subgroup of | C71×#3866⋊C3, C3×C71×#3866, C71×C3⋊#3866 |
| maximal normal subgroup of | C71×#3866⋊C3, C3×C71×#3866 |
| maximal quotient of | C3×C71×#3866, C71×C3⋊#3866 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10508, 6);