Finite Group DatabasebetaFinite Group Databasebeta| order | 10508 |
| automorphism | Aut(G) order 13240080 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D5254 |
| direct product | C2×D2627 |
| unambiguous semidirect product | (C2×C37)⋊D71 |
| unambiguous semidirect product | (C2×C71)⋊D37 |
| Fitting, socle | C2×C37×C71 ⋊ C2 |
| derived, Hall | C37×C71 ⋊ C22 |
| Sylow | C71 ⋊ C2×D37 |
| Sylow | C37 ⋊ C2×D71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2627 |
| commutator, cosocle, hypocenter | C37×C71 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C37×C71 | C2 |
| LCS | G ▷ C37×C71 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
2630 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C71⋊(D37⋊C3), D3×D2627, C2×C3×D2627, … |
| maximal normal subgroup of | C2×C71⋊(D37⋊C3), C2×C3×D2627, D10508 |
| maximal quotient of | D3×D2627, C2×C3×D2627, C2×D7881, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10508, 9);