Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C89 · Schur multiplier (H2) = C24 |
| direct product | #560×C89 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C89 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C89 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ G | |
252 conjugacy classes of subgroups.
1691 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C89×#2200, C2×#560×C89, C89×#3529, … |
| maximal normal subgroup of | C89×#2200, C2×#560×C89, C89×#3529, … |
| maximal quotient of | C89×#2375, C89×#2376, C89×#2377, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 241);