Finite Group DatabasebetaFinite Group Databasebeta| order | 6394 |
| automorphism | Aut(G) order 9706092 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3197 |
| unambiguous semidirect product | C23⋊D139 |
| unambiguous semidirect product | C139⋊D23 |
| Fitting, socle, derived, Hall | C23×C139 ⋊ C2 |
| Sylow | C139 ⋊ D23 |
| Sylow | C23 ⋊ D139 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C23×C139 | C2 |
| LCS | G ▷ C23×C139 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,23,139|b^a=b^22,c^a=c^1381600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×D139, C2×D3197, C3×D3197, … |
| maximal normal subgroup of | D23×D139, C2×D3197, C3×D3197, … |
| maximal quotient of | Dic3197, C2×D3197, C3×D3197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6394, 5);