Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3264 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C89 · Schur multiplier (H2) = C24 |
| direct product | C89×#3388 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C89 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C89 |
| prime radical | C2×D4×C89 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ C4×Q8×C89 ◁ G | |
334 conjugacy classes of subgroups.
2581 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C89×#3388, C89×#61365, C89×#61367, … |
| maximal normal subgroup of | C2×C89×#3388, C89×#61365, C89×#61367, … |
| maximal quotient of | C89×#22526, C89×#22527, C89×#22673, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 2120);