Finite Group DatabasebetaFinite Group Databasebeta| order | 5344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×Q8×C167 ⋊ C2 |
| Sylow | C167 ⋊ C22⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D167 |
| commutator, socle | C22×C167 | C23 |
| Fitting | C2×Q8×C167 | C2 |
| hypercenter | C2×Q8 | D167 |
| hypocenter | C167 | C22⋊Q8 |
| LCS | G ▷ C22×C167 ▷ C167 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
74 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,167|a^2=d,b^2=d,b^a=bd,c^a=ce,f^c=f^166844 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5344, 122);