Finite Group DatabasebetaFinite Group Databasebeta| order | 5344 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C167 · Schur multiplier (H2) = C22 |
| direct product | #99×C167 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C167 | C22⋊C4 |
| commutator | C22 | C2×C4×C167 |
| Frattini, cosocle | C23 | C22×C167 |
| prime radical | C2×D4×C167 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C167 ◁ C23×C167 ◁ G | |
52 conjugacy classes of subgroups.
1837 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AΣL(1,𝔽16)×C167, #352×C167, #353×C167, … |
| maximal normal subgroup of | AΣL(1,𝔽16)×C167, #352×C167, #353×C167, … |
| maximal quotient of | #323×C167, #324×C167, #327×C167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5344, 6);