Finite Group DatabasebetaFinite Group Databasebeta| order | 6028 |
| automorphism | Aut(G) order 4099040 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1507 |
| unambiguous semidirect product | C11⋊Dic137 |
| derived, Hall | C11×C137 ⋊ C4 |
| Sylow | C137 ⋊ Dic11 |
| Sylow | C11 ⋊ Dic137 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1507 |
| commutator, hypocenter | C11×C137 | C4 |
| Fitting, socle | C2×C11×C137 | C2 |
| LCS | G ▷ C11×C137 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,11,137,2|a^2=d,b^a=b^10,c^a=c^1361510 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic1507, Dic4521, C5×Dic1507, … |
| maximal normal subgroup of | C3×Dic1507, C5×Dic1507, (C11⋊C5)⋊Dic137, … |
| maximal quotient of | C3×Dic1507, Dic4521, C5×Dic1507, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6028, 4);