Finite Group DatabasebetaFinite Group Databasebeta| order | 9854 |
| automorphism | Aut(G) order 22348872 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4927 |
| unambiguous semidirect product | C13⋊D379 |
| unambiguous semidirect product | C379⋊D13 |
| Fitting, socle, derived, Hall | C13×C379 ⋊ C2 |
| Sylow | C379 ⋊ D13 |
| Sylow | C13 ⋊ D379 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C379 | C2 |
| LCS | G ▷ C13×C379 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,13,379|b^a=b^12,c^a=c^3782465 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D13×D379, C2×D4927, C3×D4927, … |
| maximal normal subgroup of | D13×D379, C2×D4927, C3×D4927, … |
| maximal quotient of | Dic4927, C2×D4927, C3×D4927, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9854, 3);