Finite Group DatabasebetaFinite Group Databasebeta| order | 9084 |
| automorphism | Aut(G) order 6867504 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2271 |
| unambiguous semidirect product | C3⋊Dic757 |
| derived, Hall | C3×C757 ⋊ C4 |
| Sylow | C757 ⋊ Dic3 |
| Sylow | C3 ⋊ Dic757 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2271 |
| commutator, hypocenter | C3×C757 | C4 |
| Fitting, socle | C2×C3×C757 | C2 |
| LCS | G ▷ C3×C757 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,757,2|a^2=d,b^a=b^2,c^a=c^7562274 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic6813, C3⋊(Dic757⋊C3), C3⋊Dic2271, … |
| maximal normal subgroup of | C3⋊(Dic757⋊C3), C3×Dic2271, Dic4542 |
| maximal quotient of | Dic6813, C3⋊Dic2271, C3×Dic2271, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9084, 6);