Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C137 · Schur multiplier (H2) = C28 |
| direct product | #3509×C137 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C137 |
| prime radical | C2×#41×C137 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ G | |
992 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8768 |
6028 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C137×#8427, C137×#8474, C137×#12724, … |
| maximal normal subgroup of | C137×#8427, C137×#8474, C137×#12724, … |
| maximal quotient of | C137×#34188, C137×#34209, C137×#34214, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 2241);