Finite Group DatabasebetaFinite Group Databasebeta| order | 5344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C167⋊C8) |
| Sylow | C167 ⋊ C4⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C2×D167 |
| commutator | C2×C167 | C2×C8 |
| Fitting | C42×C167 | C2 |
| socle | C22×C167 | C2×C4 |
| hypercenter | C42 | D167 |
| hypocenter | C167 | C4⋊C8 |
| LCS | G ▷ C2×C167 ▷ C167 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,167|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^1661348 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5344, 76);