Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C167 · Schur multiplier (H2) = C24 |
| direct product | C2×#99×C167 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C167 | C22⋊C4 |
| commutator | C22 | C22×C4×C167 |
| Frattini, cosocle | C23 | C23×C167 |
| prime radical | C22×D4×C167 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C167 ◁ C24×C167 ◁ G | |
210 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
3674 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 90);