Finite Group DatabasebetaFinite Group Databasebeta| order | 5954 |
| automorphism | Aut(G) order 8145072 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2977 |
| unambiguous semidirect product | C13⋊D229 |
| unambiguous semidirect product | C229⋊D13 |
| Fitting, socle, derived, Hall | C13×C229 ⋊ C2 |
| Sylow | C229 ⋊ D13 |
| Sylow | C13 ⋊ D229 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C229 | C2 |
| LCS | G ▷ C13×C229 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,13,229|b^a=b^12,c^a=c^2281490 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26045488, #26045489, D13×D229, … |
| maximal normal subgroup of | #26045488, #26045489, D13×D229, … |
| maximal quotient of | Dic2977, C2×D2977, C3×D2977, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5954, 3);