Finite Group DatabasebetaFinite Group Databasebeta| order | 10790 |
| automorphism | Aut(G) order 21234720 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5395 |
| unambiguous semidirect product | C5⋊D1079 |
| unambiguous semidirect product | C13⋊D415 |
| unambiguous semidirect product | C83⋊D65 |
| Fitting, socle, derived, Hall | C5×C13×C83 ⋊ C2 |
| Hall | C13×C83 ⋊ D5 |
| Hall | C5×C83 ⋊ D13 |
| Sylow | C83 ⋊ D65 |
| Hall | C5×C13 ⋊ D83 |
| Sylow | C13 ⋊ D415 |
| Sylow | C5 ⋊ D1079 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C13×C83 | C2 |
| LCS | G ▷ C5×C13×C83 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,13,83|b^a=b^4,c^a=c^12,d^a=d^822699 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D65×D83, D13×D415, D5×D1079, … |
| maximal normal subgroup of | D65×D83, D13×D415, D5×D1079, … |
| maximal quotient of | Dic5395, C2×D5395, C3×D5395, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10790, 8);