Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C89 · Schur multiplier (H2) = C22 |
| direct product | #339×C89 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C89 | D4 |
| commutator | C4 | C42×C89 |
| Frattini, cosocle | C22×C4 | C22×C89 |
| socle | C22×C89 | C22⋊C4 |
| prime radical | C23×C89 | D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C89 ◁ C22×C4×C89 ◁ G | |
110 conjugacy classes of subgroups.
2492 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#339×C89, C89×#1733, C4×#104×C89, … |
| maximal normal subgroup of | C2×#339×C89, C89×#1733, C4×#104×C89, … |
| maximal quotient of | C89×#1276, C89×#1278, C89×#1279, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 20);