Finite Group DatabasebetaFinite Group Databasebeta| order | 8710 |
| automorphism | Aut(G) order 13796640 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4355 |
| unambiguous semidirect product | C5⋊D871 |
| unambiguous semidirect product | C13⋊D335 |
| unambiguous semidirect product | C67⋊D65 |
| Fitting, socle, derived, Hall | C5×C13×C67 ⋊ C2 |
| Hall | C13×C67 ⋊ D5 |
| Hall | C5×C67 ⋊ D13 |
| Sylow | C67 ⋊ D65 |
| Hall | C5×C13 ⋊ D67 |
| Sylow | C13 ⋊ D335 |
| Sylow | C5 ⋊ D871 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C13×C67 | C2 |
| LCS | G ▷ C5×C13×C67 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,13,67|b^a=b^4,c^a=c^12,d^a=d^662179 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D65×D67, D13×D335, D5×D871, … |
| maximal normal subgroup of | D65×D67, D13×D335, D5×D871, … |
| maximal quotient of | Dic4355, C2×D4355, C3×D4355, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8710, 8);