Finite Group DatabasebetaFinite Group Databasebeta| order | 5516 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #11716161⋊C7 |
| Fitting, socle, derived, Sylow | C197 ⋊ C4×C7 |
| Hall | C197⋊C7 ⋊ C4 |
| Hall | #11716161 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C197 | C4×C7 |
| LCS | G ▷ C197 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,2,197|a^2=c,d^a=d^183,d^b=d^104,d^c=d^19635 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5516, 8);