Finite Group DatabasebetaFinite Group Databasebeta| order | 5344 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C167 · Schur multiplier (H2) = C1 |
| direct product | Q32×C167 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C2×C167 | D8 |
| commutator, Frattini, cosocle | C8 | C22×C167 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C167 ◁ C4×C167 ◁ C8×C167 ◁ G | |
24 conjugacy classes of subgroups.
1837 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD64×C167, Q64×C167, C2×Q32×C167, … |
| maximal normal subgroup of | SD64×C167, Q64×C167, C2×Q32×C167, … |
| maximal quotient of | #358×C167, #366×C167, C2×Q32×C167 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5344, 20);