Finite Group DatabasebetaFinite Group Databasebeta| order | 44310 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1 |
| affine general linear | AGL(1,𝔽211) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C211 | C2×C3×C5×C7 |
| LCS | G ▷ C211 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,7,211|e^a=e^210,e^b=e^196,e^c=e^107,e^d=e^171211 conjugacy classes — view the full character table.
| holomorph of | C211 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(44310, 90);