Finite Group DatabasebetaFinite Group Databasebeta| order | 5344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C22⋊D167)⋊C4 |
| Fitting | C22⋊C4×C167 ⋊ C2 |
| Sylow | C167 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D167 |
| commutator | C2×C167 | C22×C4 |
| Fitting | C22⋊C4×C167 | C2 |
| socle | C22×C167 | C23 |
| hypercenter | C22⋊C4 | D167 |
| hypocenter | C167 | C4×D4 |
| LCS | G ▷ C2×C167 ▷ C167 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,167|a^2=e,c^2=e,b^a=bd,f^c=f^166850 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5344, 106);