Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C269 · Schur multiplier (H2) = C24 |
| direct product | #556×C269 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C269 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C269 |
| prime radical | C2×D4×C269 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C269 ◁ G | |
212 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8608 |
6725 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 237);