Finite Group DatabasebetaFinite Group Databasebeta| order | 10516 |
| automorphism | Aut(G) order 12514040 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D5258 |
| direct product | C2×D2629 |
| unambiguous semidirect product | (C2×C11)⋊D239 |
| unambiguous semidirect product | (C2×C239)⋊D11 |
| Fitting, socle | C2×C11×C239 ⋊ C2 |
| derived, Hall | C11×C239 ⋊ C22 |
| Sylow | C239 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×D239 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2629 |
| commutator, cosocle, hypocenter | C11×C239 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C239 | C2 |
| LCS | G ▷ C11×C239 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
2632 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D10516, C2×D13145 |
| maximal normal subgroup of | D10516 |
| maximal quotient of | D10516, Dic5258, C2×D13145 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10516, 7);