Finite Group DatabasebetaFinite Group Databasebeta| order | 8854 |
| automorphism | Aut(G) order 18487152 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4427 |
| unambiguous semidirect product | C19⋊D233 |
| unambiguous semidirect product | C233⋊D19 |
| Fitting, socle, derived, Hall | C19×C233 ⋊ C2 |
| Sylow | C233 ⋊ D19 |
| Sylow | C19 ⋊ D233 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C233 | C2 |
| LCS | G ▷ C19×C233 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,19,233|b^a=b^18,c^a=c^2322215 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19×D233, C2×D4427, C3×D4427, … |
| maximal normal subgroup of | D19×D233, C2×D4427, C3×D4427, … |
| maximal quotient of | Dic4427, C2×D4427, C3×D4427, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8854, 3);