Finite Group DatabasebetaFinite Group Databasebeta| order | 5344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C167 ⋊ Q32 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #14581935 |
| commutator | C8×C167 | C22 |
| Frattini | C8 | C2×D167 |
| Fitting | Q16×C167 | C2 |
| socle | C2×C167 | D8 |
| hypercenter | Q16 | D167 |
| hypocenter | C167 | Q32 |
| LCS | G ▷ C8×C167 ▷ C4×C167 ▷ C2×C167 ▷ C167 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ Q16 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,167|a^2=e,b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,c^b=cd,d^b=de,f^b=f^166592 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5344, 92);