Finite Group DatabasebetaFinite Group Databasebeta| order | 9494 |
| automorphism | Aut(G) order 21836200 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4747 |
| unambiguous semidirect product | C47⋊D101 |
| unambiguous semidirect product | C101⋊D47 |
| Fitting, socle, derived, Hall | C47×C101 ⋊ C2 |
| Sylow | C101 ⋊ D47 |
| Sylow | C47 ⋊ D101 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C47×C101 | C2 |
| LCS | G ▷ C47×C101 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,47,101|b^a=b^46,c^a=c^1002375 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D47×D101, C2×D4747, C3×D4747, … |
| maximal normal subgroup of | D47×D101, C2×D4747, C3×D4747 |
| maximal quotient of | Dic4747, C2×D4747, C3×D4747, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9494, 3);