Finite Group DatabasebetaFinite Group Databasebeta| order | 4972 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#90673 |
| Fitting, socle, derived, Hall | C11×C113 ⋊ C4 |
| Sylow | C113 ⋊ Dic11 |
| Sylow | C11 ⋊ #90673 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C113 | C4 |
| LCS | G ▷ C11×C113 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,11,113|a^2=b,c^a=c^10,d^a=d^15,d^b=d^112322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4972, 7);