Finite Group DatabasebetaFinite Group Databasebeta| order | 6124 |
| automorphism | Aut(G) order 4684860 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1531 |
| unambiguous semidirect product | C1531⋊C4 |
| derived, Sylow | C1531 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1531 |
| commutator, hypocenter | C1531 | C4 |
| Fitting, socle | C2×C1531 | C2 |
| LCS | G ▷ C1531 | |
| UCS | C1 ◁ C2 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,1531|a^2=b,c^a=c^15301534 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×D1531, C2×Dic1531, C22⋊D1531, … |
| maximal normal subgroup of | C4×D1531, C2×Dic1531, C22⋊D1531, … |
| maximal quotient of | C1531⋊C8, C2×Dic1531, C3×Dic1531, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6124, 1);