Finite Group DatabasebetaFinite Group Databasebeta| order | 10274 |
| automorphism | Aut(G) order 23938420 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5137 |
| unambiguous semidirect product | C11⋊D467 |
| unambiguous semidirect product | C467⋊D11 |
| Fitting, socle, derived, Hall | C11×C467 ⋊ C2 |
| Sylow | C467 ⋊ D11 |
| Sylow | C11 ⋊ D467 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C467 | C2 |
| LCS | G ▷ C11×C467 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,11,467|b^a=b^10,c^a=c^4662570 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×D467, C2×D5137, C3×D5137, … |
| maximal normal subgroup of | D11×D467, C2×D5137, C3×D5137 |
| maximal quotient of | Dic5137, C2×D5137, C3×D5137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10274, 3);