Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C47 · Schur multiplier (H2) = C214 |
| direct product | C24×SD16×C47 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25×C47 | D4 |
| commutator, Frattini, cosocle | C4 | C26×C47 |
| prime radical | C24×D4×C47 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C25×C47 ◁ C24×C4×C47 ◁ G | |
13310 conjugacy classes of subgroups; only the 6878 normal subgroups are shown.
This group has 13310 conjugacy classes of subgroups — too many to draw. Only its 6878 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
5264 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 56066);