Finite Group DatabasebetaFinite Group Databasebeta| order | 984 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C41 ⋊ Q8 |
| Sylow | C41 ⋊ Dic6 |
| Sylow | C3 ⋊ Dic82 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×D41 |
| commutator, Fitting, socle, prime radical, cosocle | C2×C3×C41 | C22 |
| hypocenter | C3×C41 | Q8 |
| LCS | G ▷ C2×C3×C41 ▷ C3×C41 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 52 |
| transitive degree | μt(G) = 984 |
Polycyclic presentation:
2^3,3,41|a^2=c,b^2=c,b^a=bc,e^a=e^40,d^b=d^2129 conjugacy classes — view the full character table.
| maximal subgroup of | Dic6×D41, D3×Dic82, D123⋊Q8, … |
| maximal normal subgroup of | Dic6×D41, D3×Dic82, D123⋊Q8, … |
| maximal quotient of | #14520106, #14520107, Dic3⋊Dic41, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(984, 13);