Finite Group DatabasebetaFinite Group Databasebeta| order | 5344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M16×C167 ⋊ C2 |
| Sylow | C167 ⋊ #104 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22⋊D167 |
| commutator | C4×C167 | C2×C4 |
| Frattini | C2×C4 | C2×D167 |
| Fitting | M16×C167 | C2 |
| socle | C2×C167 | C22⋊C4 |
| hypercenter | M16 | D167 |
| hypocenter | C167 | #104 |
| LCS | G ▷ C4×C167 ▷ C2×C167 ▷ C167 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ M16 | |
44 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,167|a^2=d,c^2=e,d^2=e,b^a=bc,c^a=ce,c^b=ce,f^b=f^166844 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5344, 72);