Finite Group DatabasebetaFinite Group Databasebeta| order | 6302 |
| automorphism | Aut(G) order 9427792 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3151 |
| unambiguous semidirect product | C23⋊D137 |
| unambiguous semidirect product | C137⋊D23 |
| Fitting, socle, derived, Hall | C23×C137 ⋊ C2 |
| Sylow | C137 ⋊ D23 |
| Sylow | C23 ⋊ D137 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C23×C137 | C2 |
| LCS | G ▷ C23×C137 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,23,137|b^a=b^22,c^a=c^1361577 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×D137, C2×D3151, C3×D3151, … |
| maximal normal subgroup of | D23×D137, C2×D3151, C3×D3151, … |
| maximal quotient of | Dic3151, C2×D3151, C3×D3151, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6302, 3);