Finite Group DatabasebetaFinite Group Databasebeta| order | 6026 |
| automorphism | Aut(G) order 8617180 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3013 |
| unambiguous semidirect product | C23⋊D131 |
| unambiguous semidirect product | C131⋊D23 |
| Fitting, socle, derived, Hall | C23×C131 ⋊ C2 |
| Sylow | C131 ⋊ D23 |
| Sylow | C23 ⋊ D131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C23×C131 | C2 |
| LCS | G ▷ C23×C131 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,23,131|b^a=b^22,c^a=c^1301508 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×D131, C2×D3013, C3×D3013, … |
| maximal normal subgroup of | D23×D131, C2×D3013, C3×D3013, … |
| maximal quotient of | Dic3013, C2×D3013, C3×D3013, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6026, 3);