Finite Group DatabasebetaFinite Group Databasebeta| order | 5828 |
| automorphism | Aut(G) order 4021320 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1457 |
| unambiguous semidirect product | C31⋊Dic47 |
| unambiguous semidirect product | C47⋊Dic31 |
| derived, Hall | C31×C47 ⋊ C4 |
| Sylow | C47 ⋊ Dic31 |
| Sylow | C31 ⋊ Dic47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1457 |
| commutator, hypocenter | C31×C47 | C4 |
| Fitting, socle | C2×C31×C47 | C2 |
| LCS | G ▷ C31×C47 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,31,47,2|a^2=d,b^a=b^30,c^a=c^461460 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic1457, Dic4371, C47⋊((C31⋊C3)⋊C4), … |
| maximal normal subgroup of | C3×Dic1457, C47⋊((C31⋊C3)⋊C4), C5×Dic1457, … |
| maximal quotient of | C3×Dic1457, Dic4371, C5×Dic1457, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5828, 4);