Finite Group DatabasebetaFinite Group Databasebeta| order | 8930 |
| automorphism | Aut(G) order 14788080 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4465 |
| unambiguous semidirect product | C5⋊D893 |
| unambiguous semidirect product | C19⋊D235 |
| unambiguous semidirect product | C47⋊D95 |
| Fitting, socle, derived, Hall | C5×C19×C47 ⋊ C2 |
| Hall | C19×C47 ⋊ D5 |
| Hall | C5×C47 ⋊ D19 |
| Hall | C5×C19 ⋊ D47 |
| Sylow | C47 ⋊ D95 |
| Sylow | C19 ⋊ D235 |
| Sylow | C5 ⋊ D893 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C19×C47 | C2 |
| LCS | G ▷ C5×C19×C47 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,19,47|b^a=b^4,c^a=c^18,d^a=d^462234 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D47×D95, D19×D235, D5×D893, … |
| maximal normal subgroup of | D47×D95, D19×D235, D5×D893, … |
| maximal quotient of | Dic4465, C2×D4465, C3×D4465, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8930, 8);