Finite Group DatabasebetaFinite Group Databasebeta| order | 31168 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C487 · Schur multiplier (H2) = C25 |
| direct product | C2×#123×C487 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C487 | C23 |
| commutator, Frattini, cosocle | C22 | C24×C487 |
| prime radical | C22×D4×C487 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C487 ◁ G | |
342 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 15584 |
13636 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31168, 205);