Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C89 · Schur multiplier (H2) = C22 |
| direct product | C2×Q32×C89 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C89 | D8 |
| commutator, Frattini, cosocle | C8 | C23×C89 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ C2×C4×C89 ◁ C2×C8×C89 ◁ G | |
82 conjugacy classes of subgroups.
1958 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C89×#1416, C89×#1420, C4×Q32×C89, … |
| maximal normal subgroup of | C89×#1416, C89×#1420, C4×Q32×C89, … |
| maximal quotient of | C2×#358×C89, C2×#366×C89, C4×Q32×C89, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 188);