Finite Group DatabasebetaFinite Group Databasebeta| order | 6076 |
| automorphism | Aut(G) order 3827880 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1519 |
| unambiguous semidirect product | C31⋊Dic49 |
| unambiguous semidirect product | C49⋊Dic31 |
| derived, Hall | C31×C49 ⋊ C4 |
| Sylow | C49 ⋊ Dic31 |
| Sylow | C31 ⋊ Dic49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1519 |
| commutator, hypocenter | C31×C49 | C4 |
| Frattini | C2×C7 | D217 |
| Fitting | C2×C31×C49 | C2 |
| socle | C2×C7×C31 | D7 |
| LCS | G ▷ C31×C49 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,31,2,7|a^2=d,b^7=e^6,b^a=b^6e,c^a=c^30,e^a=e^61522 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C31⋊C3)⋊Dic49, (C49⋊C3)⋊Dic31, #32912004, … |
| maximal normal subgroup of | (C31⋊C3)⋊Dic49, (C49⋊C3)⋊Dic31, #32912004, … |
| maximal quotient of | C3×Dic1519, Dic4557, C5×Dic1519, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6076, 4);