Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C113 · Schur multiplier (H2) = C26 |
| direct product | C2×C4×D4×C113 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C113 | C22 |
| commutator | C2 | C23×C4×C113 |
| Frattini, cosocle | C22 | C24×C113 |
| socle | C23×C113 | C23 |
| prime radical | C22×D4×C113 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C113 ◁ G | |
426 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 274 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
4520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 196);