Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C167 · Schur multiplier (H2) = C22×C4 |
| direct product | #410×C167 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C167 | C22⋊C4 |
| commutator | C22 | C22×C4×C167 |
| Frattini, cosocle | C23 | C23×C167 |
| socle | C2×C167 | C2×C22⋊C4 |
| prime radical | C2×#41×C167 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C167 ◁ C22×C4×C167 ◁ G | |
158 conjugacy classes of subgroups.
3674 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 91);