Finite Group DatabasebetaFinite Group Databasebeta| order | 9074 |
| automorphism | Aut(G) order 18946512 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4537 |
| unambiguous semidirect product | C13⋊D349 |
| unambiguous semidirect product | C349⋊D13 |
| Fitting, socle, derived, Hall | C13×C349 ⋊ C2 |
| Sylow | C349 ⋊ D13 |
| Sylow | C13 ⋊ D349 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C349 | C2 |
| LCS | G ▷ C13×C349 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,13,349|b^a=b^12,c^a=c^3482270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31827508, #31827509, D13×D349, … |
| maximal normal subgroup of | #31827508, #31827509, D13×D349, … |
| maximal quotient of | Dic4537, C2×D4537, C3×D4537, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9074, 3);