Finite Group DatabasebetaFinite Group Databasebeta| order | 5344 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C167 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊C4×C167 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C167 | C22 |
| commutator | C2 | C22×C4×C167 |
| Frattini, cosocle | C22 | C23×C167 |
| prime radical | C24×C167 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C167 ◁ G | |
132 conjugacy classes of subgroups.
3340 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #323×C167, #342×C167, C4×C22⋊C4×C167, … |
| maximal normal subgroup of | #323×C167, #342×C167, C4×C22⋊C4×C167, … |
| maximal quotient of | C2×#95×C167, C4×C22⋊C4×C167, #379×C167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5344, 22);