Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C89 · Schur multiplier (H2) = C22 |
| direct product | C2×#330×C89 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C89 | C22⋊C4 |
| commutator | C2×C4 | C22×C4×C89 |
| Frattini, cosocle | C42 | C23×C89 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C89 ◁ C2×C42×C89 ◁ G | |
232 conjugacy classes of subgroups.
3382 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 255);