Finite Group DatabasebetaFinite Group Databasebeta| order | 10498 |
| automorphism | Aut(G) order 26454960 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5249 |
| unambiguous semidirect product | C29⋊D181 |
| unambiguous semidirect product | C181⋊D29 |
| Fitting, socle, derived, Hall | C29×C181 ⋊ C2 |
| Sylow | C181 ⋊ D29 |
| Sylow | C29 ⋊ D181 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C29×C181 | C2 |
| LCS | G ▷ C29×C181 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,29,181|b^a=b^28,c^a=c^1802626 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35230652, #35230653, D29×D181, … |
| maximal normal subgroup of | #35230652, #35230653, D29×D181, … |
| maximal quotient of | Dic5249, C2×D5249, C3×D5249, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10498, 3);