Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C167 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×C22⋊C4×C167 |
| unambiguous semidirect product | C22⋊(C42×C167) |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C167 | C22 |
| commutator | C2 | C2×C42×C167 |
| Frattini, cosocle | C23 | C23×C167 |
| socle | C23×C167 | C23 |
| prime radical | C24×C167 | C22 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C167 ◁ G | |
258 conjugacy classes of subgroups.
6680 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 58);