Finite Group DatabasebetaFinite Group Databasebeta| order | 7244 |
| automorphism | Aut(G) order 6555820 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1811 |
| unambiguous semidirect product | C1811⋊C4 |
| derived, Sylow | C1811 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1811 |
| commutator, hypocenter | C1811 | C4 |
| Fitting, socle | C2×C1811 | C2 |
| LCS | G ▷ C1811 | |
| UCS | C1 ◁ C2 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,1811|a^2=b,c^a=c^18101814 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×D1811, C2×Dic1811, C22⋊D1811, … |
| maximal normal subgroup of | C4×D1811, C2×Dic1811, C22⋊D1811, … |
| maximal quotient of | C1811⋊C8, C2×Dic1811, C3×Dic1811, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7244, 1);