Finite Group DatabasebetaFinite Group Databasebeta| order | 7708 |
| automorphism | Aut(G) order 7091360 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1927 |
| unambiguous semidirect product | C47⋊Dic41 |
| derived, Hall | C41×C47 ⋊ C4 |
| Sylow | C47 ⋊ Dic41 |
| Sylow | C41 ⋊ Dic47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1927 |
| commutator, hypocenter | C41×C47 | C4 |
| Fitting, socle | C2×C41×C47 | C2 |
| LCS | G ▷ C41×C47 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,41,47,2|a^2=d,b^a=b^40,c^a=c^461930 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic1927, Dic5781, C5×Dic1927, … |
| maximal normal subgroup of | C3×Dic1927, C5×Dic1927, C47⋊(Dic41⋊C5), … |
| maximal quotient of | C3×Dic1927, Dic5781, C5×Dic1927, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7708, 4);