Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C89 · Schur multiplier (H2) = C4 |
| direct product | #488×C89 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C89 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C89 |
| prime radical | C2×D4×C89 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ C42×C89 ◁ G | |
96 conjugacy classes of subgroups.
1958 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C89×#1414, C2×#488×C89, C89×#3131, … |
| maximal normal subgroup of | C89×#1414, C2×#488×C89, C89×#3131, … |
| maximal quotient of | C89×#1835, C89×#1933, C89×#1934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 169);