Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C137 · Schur multiplier (H2) = C211 |
| direct product | C23×C22⋊C4×C137 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25×C137 | C22 |
| commutator | C2 | C24×C4×C137 |
| Frattini, cosocle | C22 | C25×C137 |
| prime radical | C26×C137 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C25×C137 ◁ G | |
4632 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8768 |
10960 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C137×#7555, C137×#8298, C137×#10725, … |
| maximal normal subgroup of | C137×#7555, C137×#8298, C137×#10725, … |
| maximal quotient of | C23×#95×C137, C22×C4×C22⋊C4×C137, C22×#379×C137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 2151);