Finite Group DatabasebetaFinite Group Databasebeta| order | 7396 |
| automorphism | Aut(G) order 6678588 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1849 |
| unambiguous semidirect product | C1849⋊C4 |
| derived, Sylow | C1849 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1849 |
| commutator, hypocenter | C1849 | C4 |
| Frattini, socle | C2×C43 | D43 |
| Fitting | C2×C1849 | C2 |
| LCS | G ▷ C1849 | |
| UCS | C1 ◁ C2 | |
9 conjugacy classes of subgroups.
Polycyclic presentation:
2,43,2,43|a^2=c,b^43=d^42,b^a=b^42d,d^a=d^421852 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C1849⋊C3)⋊C4, C3×Dic1849, Dic5547, … |
| maximal normal subgroup of | (C1849⋊C3)⋊C4, C3×Dic1849, C5×Dic1849, … |
| maximal quotient of | C3×Dic1849, Dic5547, C5×Dic1849, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7396, 2);