Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C89 · Schur multiplier (H2) = C2 |
| direct product | C89×#1328 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C89 | #99 |
| commutator | C23 | C2×C8×C89 |
| Frattini, cosocle | C2×M16 | C22×C89 |
| socle | C2×C89 | #324 |
| prime radical | C23×C89 | C2×C8 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C89 ◁ C2×C4×C89 ◁ C2×M16×C89 ◁ G | |
90 conjugacy classes of subgroups.
2314 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 60);