Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×Q16×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2951 |
484 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|a^2=f,c^2=f,d^2=g,e^2=g,b^a=be,d^a=dg,e^a=eg,e^b=eg,h^b=h^88,d^c=dg,h^c=h^88,h^d=h^881276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36707765, #36707769, #36707776, … |
| maximal normal subgroup of | #36707765, #36707769, #36707776, … |
| maximal quotient of | #36523909, #36524136, #36524280, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 13385);