Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C89 · Schur multiplier (H2) = C28 |
| direct product | C89×#3557 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C89 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C89 |
| prime radical | #540×C89 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ G | |
930 conjugacy classes of subgroups.
3382 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C89×#61855, C89×#61856, C89×#61867, … |
| maximal normal subgroup of | C89×#61855, C89×#61856, C89×#61867, … |
| maximal quotient of | C89×#34375, C89×#34397, C89×#34421, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 2289);