Finite Group DatabasebetaFinite Group Databasebeta| order | 5084 |
| automorphism | Aut(G) order 3050400 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1271 |
| unambiguous semidirect product | C31⋊Dic41 |
| derived, Hall | C31×C41 ⋊ C4 |
| Sylow | C41 ⋊ Dic31 |
| Sylow | C31 ⋊ Dic41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1271 |
| commutator, hypocenter | C31×C41 | C4 |
| Fitting, socle | C2×C31×C41 | C2 |
| LCS | G ▷ C31×C41 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,31,41,2|a^2=d,b^a=b^30,c^a=c^401274 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic1271, Dic3813, (C31⋊C3)⋊Dic41, … |
| maximal normal subgroup of | C3×Dic1271, (C31⋊C3)⋊Dic41, C5×Dic1271, … |
| maximal quotient of | C3×Dic1271, Dic3813, C5×Dic1271, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5084, 4);