Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C89 · Schur multiplier (H2) = C22 |
| direct product | #398×C89 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C89 | C23 |
| commutator, Frattini, cosocle | C23 | C23×C89 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C89 ◁ G | |
150 conjugacy classes of subgroups.
1958 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C89×#1346, C89×#1609, C89×#1610, … |
| maximal normal subgroup of | C89×#1346, C89×#1609, C89×#1610, … |
| maximal quotient of | C89×#1441, C89×#1442, C89×#1444, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 79);