Finite Group DatabasebetaFinite Group Databasebeta| order | 10670 |
| automorphism | Aut(G) order 20486400 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5335 |
| unambiguous semidirect product | C5⋊D1067 |
| unambiguous semidirect product | C11⋊D485 |
| unambiguous semidirect product | C97⋊D55 |
| Fitting, socle, derived, Hall | C5×C11×C97 ⋊ C2 |
| Hall | C11×C97 ⋊ D5 |
| Hall | C5×C97 ⋊ D11 |
| Sylow | C97 ⋊ D55 |
| Hall | C5×C11 ⋊ D97 |
| Sylow | C11 ⋊ D485 |
| Sylow | C5 ⋊ D1067 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C11×C97 | C2 |
| LCS | G ▷ C5×C11×C97 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,11,97|b^a=b^4,c^a=c^10,d^a=d^962669 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D55×D97, D11×D485, D5×D1067, … |
| maximal normal subgroup of | D55×D97, D11×D485, D5×D1067, … |
| maximal quotient of | Dic5335, C2×D5335, C3×D5335, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10670, 9);