Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C26 |
| direct product | C2×#396×C137 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C137 | C23 |
| commutator, Frattini, cosocle | C23 | C24×C137 |
| prime radical | C25×C137 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C137 ◁ G | |
908 conjugacy classes of subgroups; only the 328 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 328 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8768 |
6028 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#396×C137, C137×#14198, C137×#14200, … |
| maximal normal subgroup of | C4×#396×C137, C137×#14198, C137×#14200, … |
| maximal quotient of | C2×#1439×C137, C2×#1441×C137, C2×#1443×C137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 1121);