Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C25 |
| direct product | C2×#398×C137 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C137 | C23 |
| commutator, Frattini, cosocle | C23 | C24×C137 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C137 ◁ G | |
692 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17536 |
6028 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C137×#9026, C137×#9027, C137×#9919, … |
| maximal normal subgroup of | C137×#9026, C137×#9027, C137×#9919, … |
| maximal quotient of | C2×#1441×C137, C2×#1442×C137, C2×#1444×C137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 1123);