Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C89 · Schur multiplier (H2) = C24 |
| direct product | #381×C89 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C89 | C23 |
| commutator | C22 | C22×C4×C89 |
| Frattini, cosocle | C23 | C23×C89 |
| prime radical | C24×C89 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C89 ◁ G | |
218 conjugacy classes of subgroups.
2492 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C89×#1284, C89×#1306, C89×#1317, … |
| maximal normal subgroup of | C89×#1284, C89×#1306, C89×#1317, … |
| maximal quotient of | C89×C22⋊#95, C89×#1434, C89×#1440, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 62);